Hessian estimates for the Lagrangian mean curvature flow

IF 2.1 2区数学 Q1 MATHEMATICS Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-17 DOI:10.1007/s00526-024-02812-7

Arunima Bhattacharya, Jeremy Wall

引用次数: 0

Abstract

In this paper, we prove interior Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian mean curvature flow under the assumption that the Lagrangian phase is hypercritical. We further extend our results to a broader class of Lagrangian mean curvature type equations.

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拉格朗日平均曲率流的赫斯估计值

在本文中，我们证明了在拉格朗日阶段是超临界的假设下，拉格朗日平均曲率流的收缩器、扩张器、平移器和旋转器的内部 Hessian 估计值。我们进一步将结果扩展到更广泛的拉格朗日平均曲率类型方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.

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