On the existence of integral currents with prescribed mean curvature vector

Duzaar F, Fuchs M (1990)

Publication Type: Journal article

Publication year: 1990

Journal

Manuscripta Mathematica Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 67

Pages Range: 41-67

Journal Issue: 1

URI: http://www.springerlink.com/content/f87239377k748433/fulltext.pdf

DOI: 10.1007/BF02568422

Abstract

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.

Authors with CRIS profile

Frank Duzaar

Involved external institutions

Rheinische Friedrich-Wilhelms-Universität Bonn DE Germany (DE)

How to cite

APA:

Duzaar, F., & Fuchs, M. (1990). On the existence of integral currents with prescribed mean curvature vector. Manuscripta Mathematica, 67(1), 41-67. https://doi.org/10.1007/BF02568422

MLA:

Duzaar, Frank, and Martin Fuchs. "On the existence of integral currents with prescribed mean curvature vector." Manuscripta Mathematica 67.1 (1990): 41-67.

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