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Harnack inequality for fractional sub-Laplacians in Carnot groups
Carnot groups heat kernel fractional powers of sub-Laplacian Harnack inequality
2012/6/21
In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a techn...
On critical cases of Sobolev's inequalities for Carnot groups
Carnot group Sobolev's inequality Brezis-Gallouet-Wainger inequality
2011/10/15
In this paper we deal with the problem of Sobolev imbedding in thecritical cases on Carnot groups. We prove some Trudinger-type inequalities on the whole Carnot group, extending to this context the Eu...
Two characterization of BV functions on Carnot groups via the heat semigroup
Functions of bounded variation perimeters Carnot groups Heat semigroup
2011/9/15
Abstract: In this paper we provide two different characterizations of sets with finite perimeter and functions of bounded variation in Carnot groups, analogous to those which hold in Euclidean spaces,...
Isoperimetric and Sobolev inequalities on hypersurfaces in sub-Riemannian Carnot groups
Carnot groups Sub-Riemannian Geometry Hypersurfaces Isoperimetric Inequality
2011/1/20
In this paper we shall study smooth submanifolds immersed in a k-step Carnot group G of homogeneous dimension Q. Our main result is an isoperimetric inequality for the case of a C2-smooth compact hype...
Carnot群上的Hopf-Lax型公式
Carnot群 粘性解 Hopf-Lax公式 拟凸
2009/9/22
文中研究了Hamilton-Jacobi方程
$u_t +H(u,Du)=0$, \ $(p,t)\in G\times (0,+\infty )$, 这里$G$是Carnot群, $Du$表示$u$的水平梯度.
当函数$H(\gamma, x)$对变量$\gamma \in R$是单调增的, 而关于变量$x\in R^m$是凸的、径向且一阶齐次时,
建立了该方程在有界连续初值$u(p,...
Horizontal Connection and Horizontal Mean Curvature in Carnot Groups
Carnot groups Nonholonomic connection Horizontal mean curvature Sub-Riemannian minimal surfaces
2007/12/13
In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli--Garofalo--Nhieu and Pauls who recently introduced sub-Riemannian minima...
Inequalities of Hadamard Type for r-Convex Functions in Carnot Groups
r-convex function extended mean values Carnot
2007/12/11
For a Carnot group G, we establish the relationshipbetween extended mean values and r-convex functions which isintroduced in this paper, which is a class of inequalities ofHadamard type for r-convex f...
Carnot-Caratheodory空间中的变换论
Carnot--Caratheodory空间 次黎曼流形 变换群
2007/12/10
Klein发表著名的埃尔兰根纲领,由群论角度研究了空间变换群的不变量,从而引进了各种不同的几何学. 本文利用Felix Klein 的观念,研究Carnot--Caratheodory空间 $\{M,Q,g\}$ (又称为次黎曼流形)上的类似问题, 给出了次黎曼流形中的共形不变量和射影不变量. 本文给出的共形和射影不变量可视为黎曼情形的一种自然推广. 由于次黎曼流形与黎曼流形之间有着本质的差异, ...