Mean Value Inequalities and Conditions to Extend Ricci Flow

نویسندگان

  • XIAODONG CAO
  • Xiaodong Cao
  • Hung Tran
چکیده

This paper concerns conditions related to the first finite singularity time of a Ricci flow solution on a closed manifold. In particular, we provide a systematic approach to the mean value inequality method, suggested by N. Le [13] and F. He [11]. We also display a close connection between this method and time slice analysis as in [23]. As an application, we prove several inequalities for a Ricci flow solution on a manifold with nonnegative isotropic curvature.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Evolution of the first eigenvalue of buckling problem on Riemannian manifold under Ricci flow

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

متن کامل

RICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...

متن کامل

Uniform Sobolev Inequalities for Manifolds Evolving by Ricci Flow

Let M be a compact n-dimensional manifold, n ≥ 2, with metric g(t) evolving by the Ricci flow ∂gij/∂t = −2Rij in (0, T ) for some T ∈ R + ∪ {∞} with g(0) = g0. Let λ0(g0) be the first eigenvalue of the operator −∆g0 + R(g0) 4 with respect to g0. We extend a recent result of R. Ye and prove uniform logarithmic Sobolev inequality and uniform Sobolev inequalities along the Ricci flow for any n ≥ 2...

متن کامل

Characterization of Pinched Ricci Curvature by Functional Inequalities

ABSTRACT. In this article, functional inequalities for diffusion semigroups on Riemannian manifolds (possibly with boundary) are established, which are equivalent to pinched Ricci curvature, along with gradient estimates, Lp-inequalities and log-Sobolev inequalities. These results are further extended to differential manifolds carrying geometric flows. As application, it is shown that they can ...

متن کامل

On quasi-Einstein Finsler spaces‎

‎The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces‎. ‎Quasi-Einstein metrics serve also as solution to the Ricci flow equation‎. ‎Here‎, ‎the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is defined‎. ‎In compact case‎, ‎it is proved that the quasi-Einstein met...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013