Results 11 to 20 of about 141 (130)
CAAI Transactions on Intelligence TechnologyMonge–Ampère equations (MAEs) are fully nonlinear second‐order partial differential equations (PDEs), which are closely related to various fields including optimal transport (OT) theory, geometrical optics and affine geometry. Despite their significance,
Xinghua Pan, Zexin Feng, Kang Yang
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Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge. [PDF]
Quant BiolAbstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Zhang P, Gao T, Guo J, Duan J.
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Geodesics in the space of relatively Kähler metrics
Journal of the London Mathematical Society, Volume 108, Issue 3, Page 1036-1081, September 2023., 2023 Abstract We derive the geodesic equation for relatively Kähler metrics on fibrations and prove that any two such metrics with fibrewise constant scalar curvature are joined by a unique smooth geodesic. We then show convexity of the log‐norm functional for this setting along geodesics, which yields simple proofs of Dervan and Sektnan's uniqueness result
Michael Hallam
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Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems
Communications on Pure and Applied Mathematics, Volume 76, Issue 8, Page 1554-1607, August 2023., 2023 Abstract For a given finite subset S of a compact Riemannian manifold (M,g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric on M\S such that each point of S corresponds to an asymptotically flat end and that the Schouten tensor of the ...
Yanyan Li, Luc Nguyen
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IET Microwaves, Antennas &Propagation, Volume 17, Issue 7, Page 547-557, June 2023., 2023 This study proposes an analytical formulation in complex coordinates to synthesise three‐dimensional single‐shell dielectric lens surfaces. An exact formulation based on geometrical optics is developed, and the synthesis problem is modelled as a non‐linear second‐order partial differential equation of the Monge–Ampère type. Abstract This study proposes
Aline Rocha de Assis +2 more
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Massively parallel computation of globally optimal shortest paths with curvature penalization
Concurrency and Computation: Practice and Experience, Volume 35, Issue 2, 25 January 2023., 2023 Abstract We address the computation of paths globally minimizing an energy involving their curvature, with given endpoints and tangents at these endpoints, according to models known as the Reeds‐Shepp car (reversible and forward variants), the Euler‐Mumford elasticae, and the Dubins car. For that purpose, we numerically solve degenerate variants of the
Jean‐Marie Mirebeau +4 more
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On Neumann problem for the degenerate Monge–Ampère type equations
Boundary Value Problems, 2021 In this paper, we study the global C 1 , 1 $C^{1, 1}$ regularity for viscosity solution of the degenerate Monge–Ampère type equation det [ D 2 u − A ( x , D u ) ] = B ( x , u , D u ) $\det [D^{2}u-A(x, Du)]=B(x, u, Du)$ with the Neumann boundary value ...
Juhua Shi, Feida Jiang
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Pracì Mìžnarodnogo Geometričnogo Centru, 2021 We study the relationship between structural properties of the two-dimensional nonconjugate subalgebras of the same rank of the Lie algebra of the Poincaré group P(1,4) and the properties of reduced equations for the (1+3)-dimensional homogeneous Monge ...
Vasyl Fedorchuk, Volodymyr Fedorchuk
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A note on second derivative estimates for Monge-Ampère-type equations
Advanced Nonlinear Studies, 2023 In this article, we revisit previous Pogorelov-type interior and global second derivative estimates of N. S. Trudinger, F. Jiang, and J. Liu for solutions of Monge-Ampère-type partial differential equations.
Trudinger Neil S.
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Convex solutions of systems arising from Monge-Ampere equations
Electronic Journal of Qualitative Theory of Differential Equations, 2009 We establish two criteria for the existence of convex solutions to a boundary value problem for weakly coupled systems arising from the Monge-Ampère equations. We shall use fixed point theorems in a cone.
Haiyan Wang
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