Article
Physics, Multidisciplinary
Mikhail V. Altaisky, Natalia E. Kaputkina, Robin Raj
Summary: This paper analyzes the use of wavelet transform in quantum field theory models written in lightfront coordinates. By generalizing the concept of continuous causal path to sequences of causally ordered spacetime regions and using wavelet transform, the evaluation rules for Feynman path integrals over such sequences are presented.
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
(2022)
Article
Astronomy & Astrophysics
E. Minguzzi
Summary: The definitions of global hyperbolicity for closed cone structures and topological preordered spaces coincide with those in recent literature on Lorentzian length spaces and Lorentzian optimal transport. In Kunzinger-Samann's Lorentzian length spaces, the definition of global hyperbolicity coincides with that for closed cone structures and topological preordered spaces.
CLASSICAL AND QUANTUM GRAVITY
(2023)
Article
Mathematics
Qi Ding
Summary: In this paper, a Liouville type theorem is obtained for the special Lagrangian equation with a certain 'convexity' condition. The strategy is to show global Hessian estimates of solutions and interior Hessian estimates on the gradient of the solutions by utilizing geometric measure theory and the Neumann-Poincare inequality on special Lagrangian graphs.
MATHEMATISCHE ANNALEN
(2023)
Article
Astronomy & Astrophysics
Pedro Bargueno
Summary: In this work, several singularity theorems applicable to the Reissner-Nordstrom spacetime are presented. Only two previous studies have predicted null incompleteness in this scenario. Additionally, it is shown that regular black holes in the Bardeen category have noncompact slices and may exhibit topology changes without the standard assumption about infinity regions.
Article
Physics, Mathematical
Benedict Schinnerl, Roland Steinbauer
Summary: In this study, we establish the Gannon-Lee theorem for non-globally hyperbolic Lorentzian metrics of C-1 regularity, the most general regularity class available in the classical singularity theorems. Additionally, we demonstrate that any maximizing causal curve in a C-1 spacetime is a geodesic and thus has C-2 regularity.
LETTERS IN MATHEMATICAL PHYSICS
(2021)
Article
Mathematics
Xiaoyang Chen, Fei Han
Summary: Bochner's classical theorem states that the isometry group of a compact Riemannian manifold with negative Ricci curvature is finite. In this paper, we provide several extensions of Bochner's theorem by allowing small positive Ricci curvature.
MATHEMATISCHE ANNALEN
(2023)
Article
History & Philosophy Of Science
Anselm Winfried Muller
Summary: The text discusses Anscombe's views on causality, emphasizing the importance of understanding specific causal expressions. It suggests that causality consists in the derivative nature of effects from their causes, but there is debate over how to interpret this concept. It also highlights the necessity of identifying a core feature of causality, as well as the significance of individual subjective consciousness of causal agency in understanding causality.
Article
Mathematics, Applied
Chuong Tran
Summary: This article discusses Leray's criterion for singularity in the Navier-Stokes equations, examines the necessary conditions and constraints for singularity, and derives the logarithmic constraint on divergence related to Leray's scaling.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Astronomy & Astrophysics
Chandrima Ganguly
Summary: A new cosmic mechanism of isotropisation in a contracting Universe is established, which does not rely on an ekpyrosis-like mechanism using an effective ultra-stiff equation of state fluid. Instead, all initially contracting, spatially homogeneous, orthogonal Bianchi Cosmologies are shown to asymptote to a spatially flat, isotropic Universe with the inclusion of a shear viscous stress.
JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS
(2021)
Article
Mathematics, Applied
Jia Xiang Wang, Bin Zhou
Summary: This paper studies the regularity of the complex Hessian equation with pole singularity on the right hand side. It demonstrates the Holder continuity of the solution to the Dirichlet problem, and improves a result from a previous study on the complex Monge-Ampere equation.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2021)
Article
Physics, Multidisciplinary
Shinsei Ryu, Junggi Yoon
Summary: We study the two-dimensional free symplectic fermion theory with antiperiodic boundary condition and address the issue of negative norm states. By introducing a new inner product, we demonstrate that this problem can be resolved. Moreover, we establish the connection between the path integral formalism and the operator formalism in deriving this new inner product. Additionally, we investigate α vacua in which the Hamiltonian appears non-Hermitian, yet the energy spectrum is found to be real. We also compare the correlation function between the α vacua and the de Sitter space.
PHYSICAL REVIEW LETTERS
(2023)
Article
Astronomy & Astrophysics
Leonardo Garcia-Heveling
Summary: The paper compares different causal structures based on three key properties and shows that spacetimes with continuous metrics do not generally admit a causal structure that satisfies all three properties simultaneously.
CLASSICAL AND QUANTUM GRAVITY
(2021)
Article
Mathematics
D. De Silva, O. Savin
Summary: In this paper, we extend the classical Krylov-Safonov Harnack inequality to consider functions with a two-scale behavior that may not satisfy an infinitesimal equation. The results have a wide range of applications in settings such as discrete difference equations, nonlocal equations, homogenization, and quasi-minimal surfaces of Almgren.
AMERICAN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Mimi Dai, Bhakti Vyas, Xiangxiong Zhang
Summary: We propose a one-dimensional (1D) model for the three-dimensional (3D) incompressible ideal magnetohydrodynamics. Local well-posedness is established for this 1D model, and a regularity criterion of the Beale-Kato-Majda type is obtained. The model with only transport effect, without the stretching effect, is shown to have a global in time strong solution. Numerical simulations suggest that solutions of the model with certain smooth periodic initial data are unlikely to develop singularities in finite time, while solutions starting from other initial data have the tendency to form singularities.
JOURNAL OF NONLINEAR SCIENCE
(2023)
Article
Mathematics, Applied
Aram Arutyunov, Dmitry Karamzin
Summary: This study investigates metric regularity and a stability theorem based on a square-root distance estimate for smooth mappings in Hilbert spaces. The main result provides a sufficient condition for this type of metric regularity and stability without the need for a priori normality assumptions. Applications include deriving Lyusternik's tangent cone theorem and the inverse function theorem in a neighborhood of abnormal points, with examples demonstrating the essence of the proposed assumptions.
SIAM JOURNAL ON OPTIMIZATION
(2021)
Article
Mathematics
Paolo Giordano, Michael Kunzinger
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
(2018)
Article
Mathematics
James D. E. Grant, Michael Kunzinger, Clemens Saemann
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
(2019)
Article
Physics, Mathematical
James D. E. Grant, Michael Kunzinger, Clemens Saemann, Roland Steinbauer
LETTERS IN MATHEMATICAL PHYSICS
(2020)
Article
Mathematics, Applied
Michael Kunzinger, Eduard A. Nigsch, Norbert Ortner
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2019)
Article
Astronomy & Astrophysics
G. Hoermann, Y. Sanchez Sanchez, C. Spreitzer, J. A. Vickers
CLASSICAL AND QUANTUM GRAVITY
(2020)
Article
Multidisciplinary Sciences
E. A. Nigsch, J. A. Vickers
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2020)
Article
Multidisciplinary Sciences
E. A. Nigsch, J. A. Vickers
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2020)
Article
Mathematics, Applied
M. Graf, M. Kunzinger, D. Mitrovic, D. Vujadinovic
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2020)
Article
Mathematics
Vyacheslav M. Boyko, Michael Kunzinger, Roman O. Popovych
Summary: The well-known solution theory for linear ordinary differential equations changes significantly when introducing an additional real parameter, with properties like the existence of fundamental sets of solutions or characterizations of such sets being sensitive to the topological properties of the underlying domain. By investigating the topological properties of the domain, a complete characterization of the solvability of parameter-dependent equations and systems can be achieved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Physics, Multidisciplinary
Michael Kunzinger, Roland Steinbauer
Summary: The null distance proposed by Sormani and Vega encodes both the manifold topology and the causality structure of a smooth spacetime. This concept is extended to Lorentzian length spaces, which generalize the Lorentzian causality theory beyond the manifold level. The article also investigates Gromov-Hausdorff convergence based on the null distance in warped product Lorentzian length spaces and provides initial results regarding its compatibility with synthetic curvature bounds.
ANNALES HENRI POINCARE
(2022)
Article
Physics, Mathematical
Michael Kunzinger, Argam Ohanyan, Benedict Schinnerl, Roland Steinbauer
Summary: This study extends the Hawking-Penrose theorem and its generalisation to Lorentzian metrics of regularity C-1. The authors address the issues of distributional Ricci tensor and lost unique solvability of geodesic equation. They develop a theory of tensor distributions of finite order to deal with the first issue and study geodesic branching and causality non-branching for the second issue. The study also provides refinements of comparison techniques used in the proof.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Michael Kunzinger, Michael Oberguggenberger, James A. Vickers
Summary: We compare two standard approaches to defining lower Ricci curvature bounds for Riemannian metrics of regularity below $C<^>2$.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
(2023)
Proceedings Paper
Mathematics, Applied
Yafet Sanchez Sanchez, James Vickers
NON-REGULAR SPACETIME GEOMETRY
(2018)
Article
Physics, Mathematical
Melanie Graf, James D. E. Grant, Michael Kunzinger, Roland Steinbauer
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2018)
