Article
Mathematics, Applied
Minsung Kim
Summary: The main result of this paper is the construction of finitely additive measures for higher rank abelian actions on Heisenberg nilmanifolds. Under a full measure set of Diophantine conditions for the generators of the action, Bufetov functionals are constructed on (2g + 1)-dimensional Heisenberg manifolds. The paper proves that the deviation of the ergodic integral of higher rank actions can be described by the asymptotic of Bufetov functionals for a sufficiently smooth function. As a corollary, the distribution of normalized ergodic integrals with variance 1 converges to a non-degenerate compactly supported measure on the real line along certain subsequences.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2022)
Article
Mathematics
Jonathan Bowden, Sebastian Hensel, Kathryn Mann, Emmanuel Militon, Richard Webb
Summary: Building on previous work [7], this study explores the action of the homeomorphism group on the fine curve graph of a surface. Unlike the classical curve graph for mapping class groups, the action of homeomorphisms on this graph exhibits a richer dynamics: parabolic isometries in addition to elliptic and hyperbolic ones, and the realization of all positive reals as asymptotic translation lengths. When the surface is a torus, the dynamics of the homeomorphism action on the fine curve graph is related to the dynamics on the torus using the classical theory of rotation sets.
ADVANCES IN MATHEMATICS
(2022)
Article
Mathematics, Applied
Qiao Liu
Summary: This paper studies a local rigidity property, where any smooth perturbations close enough to an affine action can be smoothly conjugate to the affine action with constant time change.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Biochemical Research Methods
Juan Wang, Cong-Hai Lu, Xiang-Zhen Kong, Ling-Yun Dai, Shasha Yuan, Xiaofeng Zhang
Summary: The identification of cancer types is crucial for early diagnosis and treatment of cancer. This study proposes a new low-rank subspace clustering method (MmCLRR) to effectively cluster cancer types by utilizing complementary information from cancer multi-omics data. Experimental results demonstrate its superiority in multi-view clustering.
BMC BIOINFORMATICS
(2022)
Article
Mathematics, Applied
Xiaotian Pan, Bingzhe Hou
Summary: This article focuses on left translation actions on noncommutative compact connected Lie groups and provides a topologically conjugate classification of these actions based on rotation vectors. Algebraic conjugacy and smooth conjugacy are also discussed. Additionally, it is shown that for a specific homeomorphism f, the induced isomorphism has certain properties.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Computer Science, Information Systems
Xiao Li, Min Fang, Jichuan Liu
Summary: The LEOSL method introduces a low-rank embedded orthogonal subspace learning approach to address the domain shift, hubness, and visual-semantic gap problems in zero-shot classification. By restricting mapping functions, introducing class similarity terms, and applying orthogonal constraints, the LEOSL method outperforms many state-of-the-art methods.
JOURNAL OF VISUAL COMMUNICATION AND IMAGE REPRESENTATION
(2021)
Article
Mathematics
Guoqiang Wu, Jia-Yong Wu
Summary: In this paper, various curvature-pinching conditions are provided to show compactness of shrinkers. It is proven that shrinkers with positive Ricci curvature are compact when they have bounded curvature and certain curvature-pinching conditions. It is also proven that shrinkers with certain asymptotically nonnegative sectional curvature are compact. As applications, some related classifications of shrinkers are provided.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mathematics, Applied
M. J. D. Hamilton, D. Kotschick
Summary: The study explores parallel Lagrangian foliations on Kahler manifolds, showing that a Kahler metric with a parallel Lagrangian foliation must be flat and providing examples of such foliations on closed flat Kahler manifolds that are not tori. These examples are derived from Anosov automorphisms that preserve a Kahler form.
ERGODIC THEORY AND DYNAMICAL SYSTEMS
(2021)
Article
Physics, Mathematical
George A. Elliott, Yasuhiko Sato, Klaus Thomsen
Summary: A complete characterization is provided for the KMS state spaces, considering bounded set of inverse temperatures. The findings reveal that the state spaces can be seen as arbitrary compact simplex bundles over the set of inverse temperatures, with a single point as the fiber at zero. This characterization also applies to arbitrary flows on classifiable infinite unital simple C*-algebras, with an empty fiber at zero.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
George Dimitrov, Vasil Tsanov
Summary: This paper completes the classification of hypercomplex manifolds with a compact group of automorphisms acting transitively. The description of the spaces and proofs of the results rely solely on the structure theory of reductive groups.
JOURNAL OF GEOMETRY AND PHYSICS
(2021)
Article
Mathematics
Diego Corro, Jesus Nunez-Zimbron, Masoumeh Zarei
Summary: We present an equivariant classification for orientable, closed, four-dimensional Alexandrov spaces admitting an isometric torus action, extending the equivariant classification of closed four-dimensional manifolds with torus actions by Orlik and Raymond. In addition, we demonstrate that such Alexandrov spaces are equivariantly homeomorphic to 4-dimensional Riemannian orbifolds with isometric T-2-actions, and obtain a partial homeomorphism classification.
JOURNAL OF GEOMETRIC ANALYSIS
(2022)
Article
Physics, Mathematical
Johannes Christensen, Stefaan Vaes
Summary: This paper investigates the topologically free action of a countable group on a compact metric space and its effect on the 1-cocycles and diagonal 1-parameter groups of automorphisms in the reduced crossed product C*-algebra. The study shows that the KMS spectrum, determined by the inverse temperatures, heavily depends on the nature of the acting group G.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Mathematics
Simon Brendle, Panagiota Daskalopoulos, Keaton Naff, Natasa Sesum
Summary: This paper studies the classification of ancient kappa-solutions to n-dimensional Ricci flow on Sn, extending the previous results in three dimensions. The study shows that such solutions are either isometric to a family of shrinking round spheres, or the Type II ancient solution constructed by Perelman.
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
(2023)
Article
Mathematics, Applied
Adam Kanigowski, Philipp Kunde, Kurt Vinhage, Daren Wei
Summary: We study slow entropy invariants for abelian unipotent actions U on any finite volume homogeneous space G/Gamma. For every such action, we show that the topological slow entropy can be computed directly from the dimension of a special decomposition of Lie(G) induced by Lie(U). Moreover, we prove that the metric slow entropy of the action coincides with its topological slow entropy. As a corollary, we generalize the rank one results from [14] to higher rank abelian actions.
JOURNAL OF MODERN DYNAMICS
(2022)
Article
Mathematics
Michael P. Landry
Summary: This study shows that a veering triangulation tau can determine a face sigma of the Thurston norm ball of a closed 3-manifold, and calculate the Thurston norm on the cone over sigma. Moreover, it demonstrates that tau precisely collects the taut surfaces representing classes in the cone over sigma up to isotopy. The analysis covers nonlayered veering triangulations and nonfibered faces. An analogous theorem is also proven for manifolds with boundary, which is integral to a theorem of Landry-MinskyTaylor that relates the Thurston norm to the veering polynomial, a new generalization of McMullen's Teichmuller polynomial.
ADVANCES IN MATHEMATICS
(2022)
