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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...
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...
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       font style='font-size:12px;'> 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       font style='font-size:12px;'> 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...
Analysis on Riemannian co-compact covers     co-compact covers  random       font style='font-size:12px;'> 2015/8/26
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       font style='font-size:12px;'> 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...
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...
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...
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...
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 ...
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...
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions.
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...
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...

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