Results 51 to 60 of about 1,758 (174)

The complex Monge-Ampère equation on compact Hermitian manifolds

, 2010
We show that, up to scaling, the complex Monge-Ampère equation on compact Hermitian manifolds always admits a smooth solution.
Ben Weinkove, Valentino Tosatti
core   +1 more source

On uniqueness of solutions to complex Monge–Ampère mean field equations

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3163-3180, October 2025.
Abstract We establish the uniqueness of solutions to complex Monge–Ampère mean field equations when (minus) the temperature parameter is small. In the local setting of bounded hyperconvex domains, our result partially confirms a conjecture by Berman and Berndtsson. Our approach also extends to the global context of compact complex manifolds.
Chinh H. Lu, Trong‐Thuc Phung
wiley   +1 more source

Entire solutions to the Monge–Ampère equation

, 2010
We consider the Monge–Ampère equation det(D2u)=Ψ(x,u,Du) in Rn, n⩾3, where Ψ is a positive function in C2(Rn×R×Rn). We prove the existence of convex solutions, provided there exist a subsolution of the form u̲=a|x|2 and a superharmonic bounded positive ...
Bel Kenani Toukabri, Lamia, Kallel-Jallouli, Saoussen   +1 more
core   +1 more source

Some applications of canonical metrics to Landau–Ginzburg models

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract It is known that a given smooth del Pezzo surface or Fano threefold X$X$ admits a choice of log Calabi–Yau compactified mirror toric Landau–Ginzburg model (with respect to certain fixed Kähler classes and Gorenstein toric degenerations).
Jacopo Stoppa
wiley   +1 more source

Gevrey regularity of subelliptic Monge-Ampère equations in the plane

, 2011
In this paper, we establish the Gevrey regularity of solutions for a class of degenerate Monge–Ampère equations in the plane. Under the assumptions that one principal entry of the Hessian is strictly positive and the coefficient of the equation is ...
Xu, Chao-Jiang, Li, Wei-Xi,, Chen, Hua, Lund University.   +3 more
core   +2 more sources

The properties of a new fractional g-Laplacian Monge-Ampère operator and its applications

Advances in Nonlinear Analysis
In this article, we first introduce a new fractional gg-Laplacian Monge-Ampère operator: Fgsv(x)≔infP.V.∫Rngv(z)−v(x)∣C−1(z−x)∣sdz∣C−1(z−x)∣n+s∣C∈C,{F}_{g}^{s}v\left(x):= \inf \left\{\hspace{0.1em}\text{P.V.}\hspace{0.1em}\mathop{\int }\limits_{{{\mathbb{
Wang Guotao, Yang Rui, Zhang Lihong
doaj   +1 more source

Non-Archimedean Green’s functions and Zariski decompositions

Comptes Rendus. Mathématique
We study the non-Archimedean Monge–Ampère equation on a smooth projective variety over a discretely or trivially valued field. First, we give an example of a Green’s function, associated to a divisorial valuation, which is not $\mathbb{Q}$-PL (i.e. not a
Boucksom, Sébastien, Jonsson, Mattias
doaj   +1 more source

Regularity of optimal mapping between hypercubes

Advanced Nonlinear Studies, 2023
In this note, we establish the global C3,α{C}^{3,\alpha } regularity for potential functions in optimal transportation between hypercubes in Rn{{\mathbb{R}}}^{n} for n≥3n\ge 3. When n=2n=2, the result was proved by Jhaveri.
Chen Shibing, Liu Jiakun, Wang Xu-Jia
doaj   +1 more source

Subquadratic harmonic functions on Calabi‐Yau manifolds with maximal volume growth

Communications on Pure and Applied Mathematics, Volume 77, Issue 6, Page 3080-3106, June 2024.
Abstract On a complete Calabi‐Yau manifold M$M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon‐Hein. We prove this result by proving a Liouville‐type theorem for harmonic 1‐forms, which follows from a new local L2$L^2$ estimate of the ...
Shih‐Kai Chiu
wiley   +1 more source

Aleksandrov-type estimates for a parabolic Monge-Ampere equation

Electronic Journal of Differential Equations, 2005
A classical result of Aleksandrov allows us to estimate the size of a convex function $u$ at a point $x$ in a bounded domain $Omega$ in terms of the distance from $x$ to the boundary of $Omega$ if $$int_{Omega} det D^{2}u , dx less than infty ...
David Hartenstine
doaj