SMOOTH SOLUTIONS TO ASYMPTOTIC PLATEAU TYPE PROBLEM IN HYPERBOLIC SPACE

被引：0

作者：

Sui, Zhenan ^{[1
]}

Sun, Wei ^{[2
]}

机构：

[1] Harbin Inst Technol, Inst Adv Study Math HIT, Harbin, Peoples R China

[2] ShanghaiTech Univ, Inst Math Sci, Shanghai, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2022年

关键词：

Smooth solution; asymptotic Plateau type problem; hyperbolic space; CONSTANT CURVATURE; HYPERSURFACES; EQUATIONS;

D O I：

10.3934/cpss.2022103

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate on the existence of smooth complete hypersurface with prescribed Weingarten curvature and asymptotic boundary at infinity in hyperbolic space under the assumption that there exists an asymptotic subsolution. We give an affirmative answer for the case k = n when the asymptotic boundary Gamma bounds a uniformly convex domain, and for k < n when Gamma bounds a disk, utilizing Pogorelov type interior second order estimate. Our result com- plements our previous work [12, 13], and generalizes the asymptotic Plateau type problem to non-constant prescribed curvature case.

引用

页数：17

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