Pyramid Ricci flow in higher dimensions

Generalized Ricci Flow I: Higher Derivatives Estimates for Compact Manifolds

In this paper, we consider a generalized Ricci flow and establish the higher derivatives estimates for compact manifolds. As an application, we prove the compactness theorem for this generalized Ricci flow.

Ricci Lower Bound for Kähler–ricci Flow

The Thin Viscous Flow Equation in Higher Space Dimensions

We prove local integral (entropy) estimates for nonnegative solutions of the fourth order degenerate parabolic equation u t + div(u n ru) = 0 in space dimensions two and three. These estimates enable us to show that solutions have nite speed of propagation if n 2 (1 8 ; 2) and that the support cannot shrink if the growth exponent n is larger than 3=2. In addition, we prove decay estimates for s...

Degenerate Neckpinches in Ricci Flow

In earlier work [2], we derived formal matched asymptotic profiles for families of Ricci flow solutions developing Type-II degenerate neckpinches. In the present work, we prove that there do exist Ricci flow solutions that develop singularities modeled on each such profile. In particular, we show that for each positive integer k ≥ 3, there exist compact solutions in all dimensions m ≥ 3 that be...

Ricci Flow Gravity

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar ...