Results 31 to 40 of about 5,226,204 (223)

Pluricomplex Green's functions and Fano manifolds [PDF]

Épijournal de Géométrie Algébrique, 2019
We show that if a Fano manifold does not admit Kahler-Einstein metrics then the Kahler potentials along the continuity method subconverge to a function with analytic singularities along a subvariety which solves the homogeneous complex Monge-Ampere ...
Nicholas McCleerey, Valentino Tosatti
doaj   +1 more source

On symmetry reduction and some classes of invariant solutions of the (1+3)-dimensional homogeneous Monge-Ampère equation

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
doaj   +1 more source

Generalized Liouville theorem for viscosity solutions to a singular Monge-Ampère equation

Advances in Nonlinear Analysis, 2023
In this article, we study the asymptotic behaviour at infinity for viscosity solutions to a singular Monge-Ampère equation in half space from affine geometry.
Jian Huaiyu, Wang Xianduo
doaj   +1 more source

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
wiley   +1 more source

A Free Boundary Monge–Ampère Equation and Applications to Complete Calabi–Yau Metrics [PDF]

Archive for Rational Mechanics and Analysis
Let $P$ be a convex body containing the origin in its interior. We study a real Monge-Ampère equation with singularities along $\del P$ which is Legendre dual to a certain free boundary Monge-Ampère equation.
Tristan C. Collins, Freid Tong, Shing-Tung Yau   +2 more
semanticscholar   +1 more source

Interior $C^2$ estimate for Monge-Ampère equation in dimension two [PDF]

, 2020
We obtain a genuine local $C^2$ estimate for the Monge-Ampere equation in dimension two, by using the partial Legendre transform.
Jiakun Liu
semanticscholar   +1 more source

Numerical methods for the hyperbolic Monge-Ampère equation based on the method of characteristics [PDF]

Partial Differential Equations and Applications, 2021
We present three alternative derivations of the method of characteristics (MOC) for a second order nonlinear hyperbolic partial differential equation (PDE) in two independent variables.
M. W. M. C. Bertens, E. M. Vugts, M. Anthonissen, J. H. M. ten Thije Boonkkamp, W. IJzerman   +4 more
semanticscholar   +1 more source

Convergent Semi-Lagrangian Methods for the Monge-Ampère Equation on Unstructured Grids [PDF]

SIAM Journal on Numerical Analysis, 2016
This paper is concerned with developing and analyzing convergent semi-Lagrangian methods for the fully nonlinear elliptic Monge--Ampere equation on general triangular grids.
Xiao-Bing H. Feng, Max Jensen
semanticscholar   +1 more source

Refined Boundary Behavior of the Unique Convex Solution to a Singular Dirichlet Problem for the Monge–Ampère Equation

Advanced Nonlinear Studies, 2018
This paper is concerned with the boundary behavior of the unique convex solution to a singular Dirichlet problem for the Monge–Ampère ...
Zhang Zhijun
doaj   +1 more source

The Monge–Ampère equation for non-integrable almost complex structures [PDF]

Journal of the European Mathematical Society (Print), 2016
We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.
Jianchun Chu, Valentino Tosatti, B. Weinkove   +2 more
semanticscholar   +1 more source