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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Conformally variational Riemannian invariants and their related topics
共形变分 黎曼不变量 主题
2023/4/23
It is well known that scalar curvature plays a fundamental role in general relativity. As its analogue, conformally variational Riemannian invariants (CVIs) is a category of fundamental scalar-type cu...
CONFORMAL ACTIONS OF NILPOTENT GROUPS ON PSEUDO-RIEMANNIAN MANIFOLDS
CONFORMAL ACTIONS PSEUDO-RIEMANNIAN MANIFOLDS
2015/10/14
We study conformal actions of connected nilpotent Lie groups
on compact pseudo-Riemannian manifolds. We prove that if a type-(p,q)
compact manifold M supports a conformal action of a connected nilpo...
Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams
Riemannian filling-discs van Kampen diagrams
2015/8/26
The diameter of a disc filling a loop in the universal covering of a Riemannian manifold M may be measured extrinsically using the distance function on the ambient space or intrinsically using the ind...
Small time heat kernel behavior on Riemannian complexes
Riemannian complexes kernel behavior
2015/8/26
We study how bounds on the local geometry of a Riemannian
polyhedral complex yield uniform local Poincar′e inequalities. These
inequalities have a variety of applications, including bounds on the he...
UNIFORMLY ELLIPTIC OPERATORS ON RIEMANNIAN MANIFOLDS
RIEMANNIAN MANIFOLDS ELLIPTIC OPERATORS
2015/8/26
Given a Riemannian manifold (M, g), we study the solutions of heat
equations associated with second order differential operators in divergence
form that are uniformly elliptic with respect to g . Ty...
This is a survey on analysis on non-compact co-compact Riemannian
covers and how it relates to random walks on finitely generated groups. The
focus is on the long time behavior of the heat kernel an...
On f-bi-harmonic maps between Riemannian manifolds
f-bi-harmonic maps Riemannian manifolds
2018/4/19
Abstract: Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic map...
A Critical Exponent of Fujita Type for a Nonlinear Reaction-Di usion System on Riemannian Manifold
critical exponent reaction-di usion system Riemannian manifold.
2018/4/19
In this paper, we study the global existence and nonexistence of positive solutions to the
following nonlinear reaction-di usion system
8>>>>>>>>>>>><
>>>>>>>>>>>>:
ut u = W(x)vp + S(x...
MEAN CURVATURE FLOW OF HIGHER CODIMENSION IN RIEMANNIAN MANIFOLDS
MEAN CURVATURE HIGHER CODIMENSION RIEMANNIAN MANIFOLDS
2018/4/19
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching conditio...
Invariant tensors related with natural connections for a class Riemannian product manifolds
Invariant tensors natural connections class Riemannian product manifolds Differential Geometry
2012/6/29
Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metr...
Biharmonic Semi-Riemannian Submersions from 3-manifolds
Semi-Riemannian submersions 3-manifolds Differential Geometry
2012/6/30
The main interest of the present paper is to prove the dual results for semi-Riemannian submersions, i.e., a semi-Riemannian submersion from a 3-dimensional space form into a surface is biharmonic if ...
Optimal Riemannian metric for a volumorphism and a mean ergodic theorem in complete global Alexandrov nonpositively curved spaces
Optimal Riemannian metric volumorphism mean ergodic theorem complete global Alexandrov nonpositively curved spaces Differential Geometry
2012/6/15
In this paper we give a natural condition for when a volumorphism on a Riemannian manifold $(M,g)$ is actually an isometry with respect to some other, optimal, Riemannian metric $h$. We consider the n...
Spinor formalism and the geometry of six-dimensional Riemannian spaces
Spinor formalism geometry six-dimensional Riemannian spaces Mathematical Physics
2012/4/17
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions.
Mean curvature flow of higher codimension in Riemannian manifolds
Mean curvature flow submanifolds convergence theorem curvature pinching Riemannian manifolds
2012/4/17
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching conditio...
On $(N(k),ξ)$-semi-Riemannian manifolds: Pseudosymmetries
T -curvature tensor quasi-conformal curvature tensor conformal curvature tensor conharmonic curvature tensor concircular curvature tensor
2012/3/1
Definition of $({\cal T}_{a},{\cal T}_{b})$-pseudosymmetric semi-Riemannian manifold is given. $({\cal T}_{a},{\cal T}_{b})$-pseudosy mmetric $(N(k),\xi)$-semi-Riemannian manifolds are classified. Som...