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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...
The paper deals with the asymptotic behavior as $\eps\to 0$ of the spectrum of Laplace-Beltrami operator $\Delta\e$ on the Riemannian manifold $M\e$ ($\mathrm{\dim} M\e=N\geq 2$) depending on a small ...
We consider the entropy of the solution to the heat equation on a Riemannian manifold. When the manifold is compact, we provide two estimates on the rate of change of the entropy in terms of the lower...
Given a fixed closed manifold M, we exhibit an explicit formula for the distance function of the canonical L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on M. Additionally, w...
Let M be an n-dimensional Riemannian manifold. We deal, mainly, with the problem of finding a relatively compact domain D ⊂⊂ M that minimizes Area(∂D) among domains of the same volum...
In this paper, we obtain the following generalisation of isometric C1-immersion theorem of Nash and Kuiper. Let M be a smooth manifold of dimension m and H a rank k subbundle of the tangent bundle TM ...
In this paper, we study coisotropic submanifolds of a semi-Riemannian manifold. We investigate the integrability condition of the screen distribution and give a necessary and sufficient condition on R...

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