The Conjugate Linearized Ricci Flow on Closed 3–Manifolds

نویسنده

  • MAURO CARFORA
چکیده

We characterize the conjugate linearized Ricci flow on closed three– manifolds of bounded geometry and discuss its properties. In particular, we express the evolution of the metric and of its Ricci tensor in terms of the backward heat kernel of the conjugate linearized Ricci flow. These results provide various conservation laws and monotonicity formulas for the linearized flow.

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

GEOMETRIZATION OF HEAT FLOW ON VOLUMETRICALLY ISOTHERMAL MANIFOLDS VIA THE RICCI FLOW

The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curva...

متن کامل

Harnack Estimates for Ricci Flow on a Warped Product

In this paper, we study the Ricci flow on closed manifolds equipped with warped product metric (N × F, gN + fgF ) with (F, gF ) Ricci flat. Using the framework of monotone formulas, we derive several estimates for the adapted heat conjugate fundamental solution which include an analog of G. Perelman’s differential Harnack inequality in [18].

متن کامل

Some Results for the Perelman Lyh-type Inequality

Let (M, g(t)), 0 ≤ t ≤ T , ∂M 6= φ, be a compact n-dimensional manifold, n ≥ 2, with metric g(t) evolving by the Ricci flow such that the second fundamental form of ∂M with respect to the unit outward normal of ∂M is uniformly bounded below on ∂M × [0, T ]. We will prove a global Li-Yau gradient estimate for the solution of the generalized conjugate heat equation on M × [0, T ]. We will give an...

متن کامل

Pseudolocality for the Ricci Flow and Applications

In [26], Perelman established a differential Li-YauHamilton (LYH) type inequality for fundamental solutions of the conjugate heat equation corresponding to the Ricci flow on compact manifolds (also see [23]). As an application of the LYH inequality, Perelman proved a pseudolocality result for the Ricci flow on compact manifolds. In this article we provide the details for the proofs of these res...

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 2009