Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDifferential Harnack inequalities for a family of sub-elliptic diffusion equations on Sasakian manifolds
376
0
0.0
(
0
)
Authors
Paul W.Y. Lee
Ask ChatGPT about the research
No Arabic abstract
We prove a version of differential Harnack inequality for a family of sub-elliptic diffusions on Sasakian manifolds under certain curvature conditions.
rate research
Read More
We derive estimates relating the values of a solution at any two points to the distance between the points, for quasilinear isotropic elliptic equations on compact Riemannian manifolds, depending only on dimension and a lower bound for the Ricci curvature. These estimates imply sharp gradient bounds relating the gradient of an arbitrary solution at given height to that of a symmetric solution on a warped product model space. We also discuss the problem on Finsler manifolds with nonnegative weighted Ricci curvature, and on complete manifolds with bounded geometry, including solutions on manifolds with boundary with Dirichlet boundary condition. Particular cases of our results include gradient estimates of Modica type.
We prove matrix and scalar differential Harnack inequalities for linear parabolic equations on Riemannian and Kahler manifolds.
A compact complex manifold $V$ is called Vaisman if it admits an Hermitian metric which is conformal to a Kahler one, and a non-isometric conformal action by $mathbb C$. It is called quasi-regular if the $mathbb C$-action has closed orbits. In this case the corresponding leaf space is a projective orbifold, called the quasi-regular quotient of $V$. It is known that the set of all quasi-regular Vaisman complex structures is dense in the appropriate deformation space. We count the number of closed elliptic curves on a Vaisman manifold, proving that their number is either infinite or equal to the sum of all Betti numbers of a Kahler orbifold obtained as a quasi-regular quotient of $V$. We also give a new proof of a result by Rukimbira showing that the number of Reeb orbits on a Sasakian manifold $M$ is either infinite or equal to the sum of all Betti numbers of a Kahler orbifold obtained as an $S^1$-quotient of $M$.
In this paper, we obtain some sufficient conditions for a 3-dimensional compact trans-Sasakian manifold of type $(alpha ,beta)$ to be homothetic to a Sasakian manifold. A characterization of a 3-dimensional cosymplectic manifold is also obtained.
In this work we derive local gradient and Laplacian estimates of the Aronson-Benilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound. We also prove similar results for some fast diffusion equations. Inspired by Perelmans work we discover some new entropy formulae for these equations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
