给定仿射高斯曲率的monge - ampantere方程的边界性质

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2023-11-16 DOI:10.1007/s10455-023-09933-w

Yadong Wu

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引用次数: 0

摘要

考虑给定仿射高斯曲率的monge - ampantere方程，首先在凸域上证明了中心仿射度量的完备性，推导了凸解的梯度估计，然后给出了两个Hessian特征值相对于距离函数的不同阶数。我们还证明了凸解的水平集的曲率是一致有界的，并证明了存在一类具有规定仿射高斯曲率和有界仿射主曲率的欧几里得完全双曲曲面。

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Boundary properties for a Monge-Ampère equation of prescribed affine Gauss curvature

Considering a Monge-Ampère equation with prescribed affine Gauss curvature, we first show the completeness of centroaffine metric on the convex domain and derive a gradient estimate of the convex solution and then give different orders of two eigenvalues of the Hessian with respect to the distance function. We also show that the curvature of level sets of the convex solution is uniformly bounded, and show that there exist a class of Euclidean-complete hyperbolic surfaces with prescribed affine Gauss curvature and with bounded affine principal curvatures.

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.