Results 41 to 50 of about 141 (130)

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

Local solvability of degenerate Monge-Ampere equations and applications to geometry

Electronic Journal of Differential Equations, 2007
We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These are: the problem of locally prescribed Gaussian curvature for surfaces in $mathbb{R}^{3}$, and the local
Marcus A. Khuri
doaj  

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

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

Oblique boundary value problems for augmented Hessian equations I

Bulletin of Mathematical Sciences, 2018
In this paper, we study global regularity for oblique boundary value problems of augmented Hessian equations for a class of general operators. By assuming a natural convexity condition of the domain together with appropriate convexity conditions on the ...
Feida Jiang, Neil S. Trudinger
doaj   +1 more source

Soft Kirigami Composites for Form‐Finding of Fully Flexible Deployables

Advanced Materials Technologies, Volume 9, Issue 1, January 8, 2024.
A new class of thin flexible structures are introduced that morph from flat into prescribed 3D shapes without an external stimulus such as mechanical loads or heat. To achieve control over the target shape, two different concepts are coupled: strain mismatch (inspired by biological growth) and kirigami cuts.
Jan Zavodnik, Yunbo Wang, Wenzhong Yan, Miha Brojan, Mohammad Khalid Jawed   +4 more
wiley   +1 more source

Nontrivial convex solutions for systems of Monge-Ampere equations via global bifurcation

Electronic Journal of Differential Equations, 2016
We obtain existence results for some systems of Monge-Ampere equations, using bifurcation theorems of Krasnosell'ski-Rabinowitz type.
Zexin Qi
doaj  

On partial preliminary group classification of some class of (1+3)-dimensional Monge-Ampere equations. II. Two-dimensional Lie algebras.

Pracì Mìžnarodnogo Geometričnogo Centru
We have performed the partial preliminary group classification of some class of (1+3)-dimensional Monge-Ampère equations using non-equivalent functional bases of the first-order differential invariants of two-dimensional nonconjugate subalgebras of the ...
Vasyl Fedorchuk, Volodymyr Fedorchuk
doaj   +1 more source

The regularity of solutions to the Lp Gauss image problem

Open Mathematics
The Lp{L}_{p} Gauss image problem amounts to solving a class of Monge-Ampère type equations on the sphere. In this article, we discuss the regularity of solutions to the Lp{L}_{p} Gauss image problem.
Jia Xiumei, Chen Jing
doaj   +1 more source

Symmetries, Reductions and Exact Solutions of Nonstationary Monge–Ampère Type Equations

Mathematics
A family of strongly nonlinear nonstationary equations of mathematical physics with three independent variables is investigated, which contain an arbitrary degree of the first derivative with respect to time and a quadratic combination of second ...
Alexander V. Aksenov, Andrei D. Polyanin
doaj   +1 more source