摘要
本文研究R^(n)中开子集的由几何容度刻画的几何性质,并证明两个刚性定理:若区域在其某一边界点处的任一尺度之下都具有相应的锥的容度,则该区域必定是具有相同立体角的锥体;若区域的任意边界点均满足如上容度条件,则该区域只能为半空间.
Local capacity is introduced to prove that a subset in R^(n) with the same local capacity around a boundary point as that of a cone must be a cone of the same solid angle.Consequently,we prove the rigidity of half spaces using characterizations by the local capacity.
出处
《中国科学:数学》
CSCD
北大核心
2024年第3期543-546,共4页
Scientia Sinica:Mathematica
关键词
刚性
容度
椭圆型方程
rigidity
capacity
elliptic equation