数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (1): 95-102.

• 论文 • 上一篇    下一篇

EXISTENCE OF AREA MINIMIZING TANGENT CONES OF INTEGRAL CURRENTS WITH PRESCRIBED MEAN CURVATURE

Frank Duzaar1, Martin Fuchs2   

  1. 1. Institut fur Augewandte Mathematik der Universitat Bonn, Beringstr. 4, D-53115 Bonn;
    2. Universitat des Saarlandes, Fachbereich Mathematik, D-66123 Saarbrucken
  • 收稿日期:1994-01-11 出版日期:1995-03-25 发布日期:1995-03-25

EXISTENCE OF AREA MINIMIZING TANGENT CONES OF INTEGRAL CURRENTS WITH PRESCRIBED MEAN CURVATURE

Frank Duzaar1, Martin Fuchs2   

  1. 1. Institut fur Augewandte Mathematik der Universitat Bonn, Beringstr. 4, D-53115 Bonn;
    2. Universitat des Saarlandes, Fachbereich Mathematik, D-66123 Saarbrucken
  • Received:1994-01-11 Online:1995-03-25 Published:1995-03-25

摘要: Given an integral M-currrent T0 in Rm+k and a tensor H of type(m,l)on Rm+k with values orthogonal to each of its arguments we proved in a previous paper [3] the existence of an integral m-current T=γ(M,θ.ζ)with boundary ∂T0 and mean curvature vector H by minimizing an appropriate functional on suitable subclasses of the set of all integral currents.In this paper we discuss the existence and structure of oriented tangent cones C of T at points x∈spt(T)-spt(∂T),especially we show that C is locally mass minimizing.

关键词: integral currents, generalized mean curvature, tangent cones

Abstract: Given an integral M-currrent T0 in Rm+k and a tensor H of type(m,l)on Rm+k with values orthogonal to each of its arguments we proved in a previous paper [3] the existence of an integral m-current T=γ(M,θ.ζ)with boundary ∂T0 and mean curvature vector H by minimizing an appropriate functional on suitable subclasses of the set of all integral currents.In this paper we discuss the existence and structure of oriented tangent cones C of T at points x∈spt(T)-spt(∂T),especially we show that C is locally mass minimizing.

Key words: integral currents, generalized mean curvature, tangent cones