ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS

被引：0

作者：

Tan Zhong ^{[1
]}

Wu Guochun ^{[1
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2011年 / 31卷 / 05期

关键词：

heat equation; mean curvature; higher dimensions; MINIMAL-SURFACES; H-SYSTEMS; PLATEAU; EXISTENCE;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the heat flow for the H-system with constant mean curvature in higher dimensions. We give sufficient conditions on the initial data such that the heat flow develops finite time singularity. We also provide a new set of initial data to guarantee the existence of global regular solution to the heat flow, that converges to zero in W-1,W-n with the decay rate t(2/2-n) as time goes to infinity.

引用

页码：1741 / 1748

页数：8

共 50 条

[41] UNIQUENESS THEOREM FOR SURFACES OF CONSTANT MEAN CURVATURE
RUCHERT, H
ARCHIV DER MATHEMATIK, 1979, 33 (01) : 91 - 104
[42] Parabolic stable surfaces with constant mean curvature
José M. Manzano
Joaquín Pérez
M. Magdalena Rodríguez
Calculus of Variations and Partial Differential Equations, 2011, 42 : 137 - 152
[43] DIRICHLET PROBLEM FOR SURFACES OF CONSTANT MEAN CURVATURE
SERRIN, J
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1970, 21 (SEP) : 361 - &
[44] Constant mean curvature surfaces with three ends
Grosse-Brauckmann, K
Kusner, RB
Sullivan, JM
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2000, 97 (26) : 14067 - 14068
[45] Constant mean curvature surfaces with Delaunay ends
Mazzeo, R
Pacard, F
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2001, 9 (01) : 169 - 237
[46] Constant mean curvature surfaces bounded by a circle
López, R
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1999, 29 (03) : 971 - 978
[47] Timelike Constant Mean Curvature Surfaces with Singularities
Brander, David
Svensson, Martin
JOURNAL OF GEOMETRIC ANALYSIS, 2014, 24 (03) : 1641 - 1672
[48] AN A PRIORI BOUND FOR SURFACES OF CONSTANT MEAN CURVATURE
SERRIN, JB
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (07): : 1075 - &
[49] ON REGULARITY OF GENERALIZED SURFACES OF CONSTANT MEAN CURVATURE
GULLIVER, R
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 77 (02) : 243 - &
[50] Delaunay ends of constant mean curvature surfaces
Kilian, M.
Rossman, W.
Schmitt, N.
COMPOSITIO MATHEMATICA, 2008, 144 (01) : 186 - 220

← 1 2 3 4 5 →