Results 51 to 60 of about 2,338 (154)

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

Removable Singularities of $m$-Hessian Equations

, 2016
In this paper we give a new, less restrictive condition for removability of singular sets, $E$, of smooth solutions to the m-Hessian equation (and also for more general fully nonlinear elliptic equations) in $\Omega \setminus E$, $\Omega \subset \mathbb ...
Car, Hülya, Pröpper, René
core   +1 more source

On the Moser-Trudinger inequality in complex space

, 2018
In this paper we prove the pluricomplex counterpart of the Moser-Trudinger and Sobolev inequalities in complex space. We consider these inequalities for plurisubharmonic functions with finite pluricomplex energy, and we estimate the concerned ...
Ahag, Per, Czyz, Rafal
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

From Monge-Ampere equations to envelopes and geodesic rays in the zero temperature limit [PDF]

, 2017
Let X be a compact complex manifold equipped with a smooth (but not necessarily positive) closed form theta of one-one type. By a well-known envelope construction this data determines a canonical theta-psh function u which is not two times differentiable,
Berman, Robert J.
core  

Adapted complex tubes on the symplectization of pseudo-Hermitian manifolds

, 2010
Let $(M,\omega)$ be a pseudo-Hermitian space of real dimension $2n+1$, that is $\RManBase$ is a $\CR-$manifold of dimension $2n+1$ and $\omega$ is a contact form on $M$ giving the Levi distribution $HT(M)\subset TM$.
Tomassini, Giuseppe, Venturini, Sergio
core   +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

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