The weighted isoperimetric-type and Sobolev-type inequalities for hypersurfaces in Carnot groups

被引：4
|
作者：
He, Guoqing [1 ,2 ]
Zhao, Peibiao [1 ]
机构：
[1] Nanjing Univ Sci & Technol, Sch Sci, Nanjing 210094, Jiangsu, Peoples R China
[2] Anhui Normal Univ, Sch Math & Comp Sci, Wuhu 241000, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 135卷
关键词：
Weighted isoperimetric-type inequality; Weighted Sobolev-type inequality; Carnot group; REGULAR HYPERSURFACES; INTRINSIC PERIMETER; REPRESENTATION; FORMULAS; RECTIFIABILITY; GEOMETRY; THEOREM;
D O I：
10.1016/j.na.2015.12.029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper mainly studies hypersurfaces immersed in a sub-Riemannian step k Carnot group G with a density e(f), where f is a smooth function on G. We give the first variation formula about the weighted horizontal area of hypersurfaces. Furthermore on the base of some work we derive the weighted isoperimetric-type and Sobolev-type inequalities for hypersurfaces. (C) 2016 Elsevier Ltd. All rights reserved.
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页码：35 / 56
页数：22
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