The Soliton-Ricci Flow with variable volume forms

P-forms and Ricci Flow with Bounded Curvature on Manifolds

In this paper, we study the evolution of L p-forms under Ricci flow with bounded curvature on a complete non-compact or a compact Riemannian manifold. We show that under curvature pinching conditions on such a manifold, the L norm of a smooth p-form is non-increasing along the Ricci flow. The L∞ norm is showed to have monotonicity property too.

A note on Kähler-Ricci soliton

In this note we provide a proof of the following: Any compact KRS with positive bisectional curvature is biholomorphic to the complex projective space. As a corollary, we obtain an alternative proof of the Frankel conjecture by using the Kähler-Ricci flow. The purpose of this note is to give a proof of the following theorem, which does not rely on the previous solutions of Frankel conjecture: T...

Ricci Lower Bound for Kähler–ricci Flow

Numerical Kähler-Ricci soliton on the second del Pezzo

The second del Pezzo surface is known by work of Tian-Zhu and Wang-Zhu to admit a unique Kähler-Ricci soliton. Applying a method described in hep-th/0703057, we use Ricci flow to numerically compute that soliton metric. We numerically compute the value of its Perelman entropy (or Gaussian density). In a recent paper [1], Doran, Herzog, Kantor, and the present authors presented several numerical...

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...