ON THE EXISTENCE OF INTEGRAL CURRENTS WITH PRESCRIBED MEAN-CURVATURE VECTOR

被引：17

作者：

DUZAAR, F ^{[1
]}

FUCHS, M ^{[1
]}

机构：

[1] UNIV DUSSELDORF,INST MATH,W-4000 DUSSELDORF 1,GERMANY

来源：

MANUSCRIPTA MATHEMATICA | 1990年 / 67卷 / 01期

关键词：

49F20; 49F22; 53A10; AMS-classification; generalized mean curvature; integral currents; isoperimetric inequality; stationary varifolds;

D O I：

10.1007/BF02568422

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given an integral m-current T 0 in ℝ m+k and a tensor H of typ (m, 1) on ℝ m+k with values orthogonal to each of its arguments we prove the existence of an integral m-current T with boundary ∂T=∂T 0 having prescribed mean curvature vector H, i. e. {Mathematical expression} is a solution of[Figure not available: see fulltext.] for all vectorfields X: ℝ m+k → ℝ m+k with spt(X)∩spt(∂T)=Ø. It turns out that we can solve the above equation assuming {Mathematical expression} where γ m denotes the constant of Almgren's Isoperimetric Theorem and {Mathematical expression} is an integral m-current minimizing mass for the boundary ∂T 0. © 1990 Springer-Verlag.

引用

页码：41 / 67

页数：27

共 20 条

[1] FIRST VARIATION OF A VARIFOLD [J].