Results 41 to 50 of about 2,184 (136)
Singular structures in solutions to the Monge-Ampère equation with point masses
Mathematics in Engineering, 2023 We construct new examples of Monge-Ampère metrics with polyhedral singular structures, motivated by problems related to the optimal transport of point masses and to mirror symmetry.
Connor Mooney , Arghya Rakshit
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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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The complex Monge-Amp\`{e}re equation on some compact Hermitian manifolds
, 2014 We consider the complex Monge-Amp\`{e}re equation on compact manifolds when the background metric is a Hermitian metric (in complex dimension two) or a kind of Hermitian metric (in higher dimensions).
Chu, Jianchun
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Dispersionless Hirota equations and the genus 3 hyperelliptic divisor [PDF]
, 2019 Equations of dispersionless Hirota type have been thoroughly investigated in the mathematical physics and differential geometry literature. It is known that the parameter space of integrable Hirota type equations in 3D is 21-dimensional and the action of
Cléry, Fabien, Ferapontov, Evgeny V.
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AIMS Mathematics, 2023 In the present paper, we prove the a priori bounds and existence of smooth solutions to a Minkowski type problem for the log-concave measure $ e^{-f(|x|^2)}dx $ in warped product space forms with zero sectional curvature. Our proof is based on the method
Zhengmao Chen
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Convergence of the weak K\"ahler-Ricci Flow on manifolds of general type
, 2019 We study the K\"ahler-Ricci flow on compact K\"ahler manifolds whose canonical bundle is big. We show that the normalized K\"ahler-Ricci flow has long time existence in the viscosity sense, is continuous in a Zariski open set, and converges to the unique
Tô, Tat Dat
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Initial design with L2 Monge-Kantorovich theory for the Monge–Ampère equation method of freeform optics [PDF]
, 2014 The Monge–Ampère (MA) equation arising in illumination design is highly nonlinear so that the convergence of the MA method is strongly determined by the initial design.
Benitez Gimenez, Pablo +3 more
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The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies [PDF]
, 2004 Using methods of geometry and cohomology developed recently, we study the Monge-Ampère equation, arising as the first nontrivial equation in the associativity equations, or WDVV equations. We describe Hamiltonian and symplectic structures as well as
Kersten, P.H.M. +2 more
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Numerical solution of the simple Monge–Ampère equation with nonconvex dirichlet data on non-convex domains [PDF]
, 2017 The existence of a unique numerical solution of the semi-Lagrangian method for the simple Monge-Ampere equation is known independently of the convexity of the domain or Dirichlet boundary data - when the Monge-Ampere equation is posed as a Bellman ...
Jensen, Max
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Dimer models and conformal structures
Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 340-446, February 2026.Abstract Dimer models have been the focus of intense research efforts over the last years. Our paper grew out of an effort to develop new methods to study minimizers or the asymptotic height functions of general dimer models and the geometry of their frozen boundaries.
Kari Astala +3 more
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