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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Steady gradient Ricci solitons with positive curvature
正曲率 稳态梯度 利玛窦孤子
2023/4/17
We will construct some new examples of steady gradient Ricci solitons with positive curvature operator. Moreover, for any 3D steady gradient Ricci soliton with positive curvature, if it is asymptotic ...
Square complexes and simplicial nonpositive curvature
Square complexes simplicial nonpositive curvature Group Theory
2011/9/16
Abstract: We prove that each nonpositively curved square VH-complex can be turned functorially into a locally 6-large simplicial complex of the same homotopy type. It follows that any group acting geo...
Equivalent Semigroup Properties for Curvature-Dimension Condition
Curvature-dimension condition gradient inequality Harnack inequality
2011/2/28
Some equivalent gradient and Harnack inequalities of a diffusion semigroup are presented for the curvature-dimension condition of the associated generator. As ap-plications, the first eigenvalue, the ...
Surfaces with parallel mean curvature in $\mathbb{C}P^n\times\mathbb{R}$ and $\mathbb{C}H^n\times\mathbb{R}$
Surfaces with parallel mean curvature math
2010/11/24
We consider surfaces with parallel mean curvature vector (pmc surfaces) in $\mathbb{C}P^n\times\mathbb{R}$ and $\mathbb{C}H^n\times\mathbb{R}$, and, more generally, in cosymplectic space forms. We in...
Flows of constant mean curvature tori in the 3-sphere: The equivariant case
curvature tori the 3-sphere
2010/11/18
We present a deformation for constant mean curvature tori in the 3-sphere. We show that the moduli space of equivariant constant mean curvature tori in the 3-sphere is connected, and we classify the m...
Generalized $1$-harmonic Equation and The Inverse Mean Curvature Flow
Generalized $1$-harmonic Equation The Inverse Mean Curvature Flow
2010/11/19
We introduce and study generalized $1$-harmonic equations (1.1). Using some ideas and techniques in studying $1$-harmonic functions from [W1] (2007), and in studying nonhomogeneous $1$-harmonic funct...
Integral Menger curvature for sets of arbitrary dimension in $\mathbb{R}^n$. Part I: Uniform Ahlfors regularity
Integral Menger curvature math
2010/11/15
We propose the notion of integral Menger curvature for $m$-dimensional sets in $n$-dimensional Euclidean space and prove that finiteness of this quantity implies Ahlfors regularity with constant depe...
A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities
Lie algebraic Ricci flow invariant curvature conditions Harnack inequalities
2010/11/22
We consider a subset $S$ of the complex Lie algebra $\so(n,\C)$ and the cone $C(S)$ of curvature operators which are nonnegative on $S$. We show that $C(S)$ defines a Ricci flow invariant curvature co...
Existence of translating solutions to the flow by powers of mean curvature on unbounded domains
Dirichlet problem mean curvature flow elliptic equation unbounded domain.
2010/12/7
In this paper, we prove the existence of classical solutions of the Dirichlet problem for a class of quasi-linear elliptic equations on unbounded domains like a cone or a U-type domain in Rn(n ≥ 2). T...
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...
