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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
2023/4/21
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
2013/5/24
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.
2012/12/12
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
2012/6/13
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
2012/6/8
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
2012/6/8
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
2012/6/2
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...
Mean curvature flow of higher codimension in Riemannian manifolds
Mean curvature flow submanifolds convergence theorem curvature pinching Riemannian manifolds
2012/3/31
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
2012/2/29
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...
Index of quasi-conformally symmetric semi-Riemannian manifolds
Index of a semi-Riemannian manifold metric connection quasi-conformal curvature tensor
2012/2/28
We find the index of $\widetilde{\nabla}$-quasi-conformally symmetric and $\widetilde{\nabla}$-concircularly symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is metric connection.