Article
Mathematics, Applied
Miguel Brozos-Vazquez, Diego Mojon-Alvarez
Summary: We study the geometric structure of weighted Einstein smooth metric measure spaces with weighted harmonic Weyl tensor. A complete local classification is provided, showing that either the underlying manifold is Einstein, or decomposes as a warped product in a specific way. Moreover, if the manifold is complete, then it either is a weighted analogue of a space form, or it belongs to a particular family of Einstein warped products.
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2024)
Article
Mathematics
Lanbao Hou, Feng Du, Jing Mao, Chuanxi Wu
Summary: This paper studies the eigenvalue problem under specific conditions and obtains several universal inequalities.
Article
Mathematics, Applied
Bobo Hua, Jia-Yong Wu
Summary: In this paper, two gap theorems are established for the ends of smooth metric measure space with specific conditions, providing insights into the boundary properties of these spaces.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Yanlin Li, Dipen Ganguly, Santu Dey, Arindam Bhattacharyya
Summary: This paper discusses the class of epsilon-Kenmotsu manifolds that have conformal eta-Ricci solitons. It studies the special types of Ricci tensor associated with conformal eta-Ricci solitons on epsilon-Kenmotsu manifolds. Additionally, it investigates curvature conditions that allow for conformal eta-Ricci solitons on epsilon-Kenmotsu manifolds. Furthermore, the paper presents a characterization of the potential function for gradient conformal eta-Ricci solitons. Lastly, an illustrative example is provided to demonstrate the existence of conformal eta-Ricci solitons on eta-Kenmotsu manifolds.
Article
Mathematics, Applied
Cornelia-Livia Bejan, Galia Nakova, Adara M. Blaga
Summary: In this article, we study some corresponding results from the Kahlerian and para-Kahlerian context concerning the Bochner curvature on a Kahler B-manifold (i.e., a Kahler manifold with a Norden metric). We prove that such a manifold is of constant totally real sectional curvatures if and only if it is a holomorphic Einstein, Bochner flat manifold. Moreover, we provide the necessary and sufficient conditions for a gradient Ricci soliton or a holomorphic ?-Einstein Kahler manifold with a Norden metric to be Bochner flat. Finally, we show that a Kahler B-manifold is of quasi-constant totally real sectional curvatures if and only if it is a holomorphic ?-Einstein, Bochner flat manifold.
Article
Mathematics
Xinyue Cheng, Hong Cheng
Summary: In this paper, the authors mainly focus on the study of weakly weighted Einstein-Finsler metrics. They first prove that weakly weighted Einstein-Kropina metrics must have isotropic S-curvature with respect to the Busemann-Hausdorff volume form under certain conditions about the weight constants. Then they characterize weakly weighted Einstein-Kropina metrics completely using their navigation expressions or the values of a and 0. Particularly, when v ? 0 (or v = K = 0), and the S-curvature with respect to the Busemann-Hausdorff volume form is isotropic, they show that a Kropina metric determined by navigation data (h, W) is a weakly weighted Einstein metric if and only if the Riemann metric h is a weighted Einstein-Riemann metric.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mathematics
Cornelia-Livia Bejan, Semsi Eken Meric, Erol Kilic
Summary: This paper mainly deals with a contact-complex Riemannian submersion from an eta-Ricci soliton, studying cases when the base manifold is Einstein and when the fibers are eta-Einstein submanifolds. Additionally, some results regarding the potential are obtained in this study.
Article
Mathematics, Applied
Vladimir Rovenski, Robert Wolak
Summary: The study focuses on the Ricci curvature properties of g-manifolds, particularly in the case of higher dimensional abelian Lie algebras. It investigates the relationship between the Ricci curvature of the manifold and the Ricci curvature of the transverse manifold of the characteristic foliation. Additionally, sufficient conditions for a g-manifold to be a Ricci soliton or gradient Ricci soliton are identified, and a surprising higher dimensional generalization of the Boyer-Galicki theorem on Einstein K-manifolds is obtained for a special class of abelian g-manifolds.
JOURNAL OF GEOMETRY AND PHYSICS
(2021)
Article
Mathematics
Yanlin Li, Dhriti Sundar Patra, Nadia Alluhaibi, Fatemah Mofarreh, Akram Ali
Summary: This article investigates the geometric classification and properties of k-almost Ricci solitons associated with paracontact manifolds, and derives some conclusions.
Article
Chemistry, Physical
D. Vijay Anand, Qiang Xu, JunJie Wee, Kelin Xia, Tze Chien Sum
Summary: Accelerated materials development with machine learning and high throughput experimentation is crucial for addressing energy challenges. In the field of perovskite materials design, learning models based on persistent functions offer improved accuracy and performance comparable to deep learning models. The multiscale simplicial complex approach provides a precise representation for structures and interactions, enhancing transferability to machine learning models. Advanced geometrical and topological invariants are efficient feature engineering approaches that greatly improve the performance of learning models for molecular data analysis.
NPJ COMPUTATIONAL MATERIALS
(2022)
Article
Mathematics, Applied
Mancho Manev
Summary: This paper introduces and studies Ricci-like solitons with arbitrary potential on Sasaki-like almost contact B-metric manifolds. The soliton is characterized by the property that its Ricci tensor is equal to the vertical component of both B-metrics multiplied by a constant. Several conclusions are derived based on this property, and explicit examples are provided.
RESULTS IN MATHEMATICS
(2022)
Article
Mathematics, Applied
Xiaohuan Mo, Hongmei Zhu, Ling Zhu
Summary: In this paper, the authors study a class of Finsler measure spaces whose weighted Ricci curvature satisfies Ric infinity = cF2. This class includes all gradient Ricci solitons and Finsler Gaussian shrinking solitons. Therefore, Finsler measure spaces in this class are called Finsler gradient Ricci solitons. The authors also find sufficient and necessary conditions for a Randers measure space to be a Finsler gradient Ricci soliton and prove that Randers-Finsler gradient Ricci solitons must have isotropic S-curvature. They also provide an equivalent condition for a Randers measure space to be a Finsler gradient Ricci soliton of constant S-curvature.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Xinyue Cheng, Zhongmin Shen
Summary: In this paper, we establish some important inequalities on Finsler manifolds under a lower weighted Ricci curvature bound. These include a relative volume comparison, an upper bound for volumes, a Bonnet-Myers type theorem, and a sharp Poincare-Lichnerowicz inequality.
RESULTS IN MATHEMATICS
(2022)
Article
Physics, Multidisciplinary
Santu Dey, Nasser Bin Turki
Summary: The goal of this study is to investigate the *-eta-Ricci soliton and gradient almost *-eta-Ricci soliton within the framework of para-Kenmotsu manifolds as a characterization of Einstein metrics. The study shows that a para-Kenmotsu metric is an Einstein metric if the soliton vector field is contact. The nature of the soliton and the scalar curvature are also discussed when a para-Kenmotsu manifold admits a *-eta-Ricci soliton.
FRONTIERS IN PHYSICS
(2022)
Article
Mathematics, Applied
Bin Shen, Zisu Zhao
Summary: The paper generalizes the Myers theorem on Finsler manifolds with four different curvature conditions, and also provides the generalized Myers theorem on weighted Riemannian manifolds.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Jeffrey S. Case
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2017)
Article
Mathematics
Jeffrey S. Case, Sean N. Curry, Vladimir S. Matveev
COMPTES RENDUS MATHEMATIQUE
(2018)
Article
Mathematics
Jeffrey S. Case
INDIANA UNIVERSITY MATHEMATICS JOURNAL
(2018)
Article
Mathematics
Jeffrey S. Case, Yi Wang
ADVANCES IN MATHEMATICS
(2018)
Article
Mathematics
Jeffrey S. Case, Yi Wang
JOURNAL OF FUNCTIONAL ANALYSIS
(2018)
Article
Mathematics, Applied
Jeffrey S. Case, Jih-Hsin Cheng, Paul Yang
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2019)
Article
Mathematics, Applied
Jeffrey S. Case, Chin-Yu Hsiao, Paul Yang
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2019)
Article
Mathematics, Applied
Jeffrey S. Case, Ana Claudia Moreira, Yi Wang
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2019)
Article
Mathematics
Jeffrey S. Case, Weiyu Luo
Summary: This paper introduces a set of conformally covariant boundary operators associated with the 6th-order Graham-Jenne-Mason-Sparling (GJMS) operator, which can be applied to a conformally invariant class of manifolds such as compactifications of Poincare-Einstein manifolds, providing a conformally covariant energy functional for the 6th-order GJMS operator on these manifolds. Additionally, the boundary operators allow the realization of fractional GJMS operators of order one, three, and five as generalized Dirichlet-to-Neumann operators, leading to the proof of some sharp Sobolev trace inequalities.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2021)
Article
Mathematics, Applied
Jeffrey S. Case
Summary: Frank and Lieb provided a new proof of the sharp Hardy-Littlewood-Sobolev inequalities by using conformal covariance, and also presented new proofs for Sobolev inequalities. Furthermore, they showed a direct proof of certain inequalities without going through the Hardy-Littlewood-Sobolev inequalities, and a new proof for a sharp fully nonlinear Sobolev inequality involving sigma 2-curvature. Their argument was based on commutator identities derived using the Fefferman-Graham ambient metric.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2021)
Article
Mathematics
Jeffrey S. Case
JOURNAL OF FUNCTIONAL ANALYSIS
(2020)
Article
Mathematics
Jeffrey S. Case, Paul Yang
Summary: We have proven rigidity for the Lichnerowicz-type eigenvalue estimate for the Kohn Laplacian on strictly pseudoconvex three manifolds with nonnegative CR Paneitz operator and positive Webster curvature. This conditions for this rigidity include the manifold having a nonnegative CR Paneitz operator and positive Webster curvature.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics, Applied
Jeffrey S. Case
Summary: This article introduces a natural conformally invariant form that is closely related to the Pfaffian of the Weyl tensor and top degree Pontrjagin forms. It discusses the properties and functions of these forms on manifolds.
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
(2022)
Article
Mathematics
Jeffrey S. Case, Yi Wang
JOURNAL OF MATHEMATICAL STUDY
(2020)
Article
Mathematics
Jeffrey S. Case, Yueh-Ju Lin, Wei Yuan
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2019)
Article
Mathematics
Matija Bucic, Richard Montgomery
Summary: This article improves upon previous research by showing that any n-vertex graph can be decomposed into O(n log* n) cycles and edges.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Laurentiu G. Maxim, Jose Israel Rodriguez, Botong Wang, Lei Wu
Summary: The paper investigates the relationship between linear optimization degree and geometric structure. By analyzing the geometric structure of the conormal variety of an affine variety, the Chern-Mather classes of the given variety can be completely determined. Additionally, the paper shows that these bidegrees coincide with the linear optimization degrees of generic affine sections.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
William Chan, Stephen Jackson, Nam Trang
Summary: Under the determinacy hypothesis, this paper completely characterizes the existence of nontrivial maximal almost disjoint families for specific cardinals kappa, considering the ideals of bounded subsets and subsets of cardinality less than kappa.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Zhenguo Liang, Zhiyan Zhao, Qi Zhou
Summary: This paper investigates the reducibility of the one-dimensional quantum harmonic oscillator perturbed by a time quasi-periodic quadratic form. It provides a description and upper bound for the growth of the Sobolev norms of the solution, and demonstrates the optimality of the upper bound.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Zhao Yu Ma, Yair Shenfeld
Summary: This study provides a new approach to understanding the extremal cases of Stanley's inequalities by establishing a connection between the combinatorics of partially ordered sets and the geometry of convex polytopes.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Laurent Laurent, Rosa M. Miro-Roig
Summary: This paper discusses the problem of constructing matrices of linear forms of constant rank by focusing on vector bundles on projective spaces. It introduces important examples of classical Steiner bundles and Drezet bundles, and uses the classification of globally generated vector bundles to describe completely the indecomposable matrices of constant rank up to six.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Nicoletta Cantarini, Fabrizio Caselli, Victor Kac
Summary: In this paper, we construct a duality functor in the category of continuous representations to study the Lie superalgebra E(4, 4). By constructing a specific type of Lie conformal superalgebra, we obtain that E(4, 4) is its annihilation algebra. Furthermore, we also obtain an explicit realization of E(4, 4) on a supermanifold in the process of studying.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Rotem Assouline, Bo'az Klartag
Summary: This article studies the horocyclic Minkowski sum of two subsets in the hyperbolic plane and its properties. It proves an inequality relating the area of the subsets when they are Borel-measurable, and provides a connection to other inequalities.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Alessio Porretta
Summary: This article discusses Fokker-Planck equations driven by Levy processes in the entire Euclidean space, under the influence of confining drifts, similar to the classical Ornstein-Ulhenbeck model. A new PDE method is introduced to obtain exponential or sub-exponential decay rates of zero average solutions as time goes to infinity, under certain diffusivity conditions on the Levy process, including the fractional Laplace operator as a model example. The approach relies on long-time oscillation estimates of the adjoint problem and applies to both local and nonlocal diffusions, as well as strongly or weakly confining drifts.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Weichao Qian, Yong Li, Xue Yang
Summary: In this paper, we investigate the persistence of resonant invariant tori in Hamiltonian systems with high-order degenerate perturbation, and prove a quasiperiodic Poincare theorem under high degeneracy, answering a long-standing conjecture on the persistence of resonant invariant tori in general situations.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Julius Ross, David Witt Nystroem
Summary: This article extends Prekopa's Theorem and the Brunn-Minkowski Theorem from convexity to F-subharmonicity, and applies it to the interpolation problem of convex functions and convex sets, introducing a new notion of harmonic interpolation.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Airi Takeuchi, Lei Zhao
Summary: In this article, we explore the connection between several integrable mechanical billiards in the plane through conformal transformations. We discuss the equivalence of free billiards and central force problems, as well as the correspondence between integrable Hooke-Kepler billiards. We also investigate the integrability of Kepler billiards and Stark billiards, and the relationship between billiard systems and Euler's two-center problems.
ADVANCES IN MATHEMATICS
(2024)
Article
Mathematics
Damiano Rossi
Summary: In this study, we prove new results in generalised Harish-Chandra theory by providing a description of the Brauer-Lusztig blocks using the p-adic cohomology of Deligne-Lusztig varieties. We then propose new conjectures for finite reductive groups by considering geometric analogues of the p-local structures. Our conjectures coincide with the counting conjectures for large primes, thanks to a connection established between p-structures and their geometric counterparts. Finally, we simplify our conjectures by reducing them to the verification of Clifford theoretic properties.
ADVANCES IN MATHEMATICS
(2024)
