Ricci flow of negatively curved incomplete surfaces

Giesen, Gregor; Topping, Peter M.
July 2010
Calculus of Variations & Partial Differential Equations;Jul2010, Vol. 38 Issue 3/4, p357
Academic Journal
We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the issue of well-posedness in this class.


Related Articles

  • Maximum Solutions of Normalized Ricci Flow on 4-Manifolds. Fang, Fuquan; Zhang, Yuguang; Zhang, Zhenlei // Communications in Mathematical Physics;Sep2008, Vol. 283 Issue 1, p1 

    We consider the maximum solution g( t), t ? [0, + 8), to the normalized Ricci flow. Among other things, we prove that, if ( M, ?) is a smooth compact symplectic 4-manifold such that $${b_2^+(M) > 1}$$ and let g( t), t ? [0, 8), be a solution to (1.3) on M whose Ricci curvature satisfies that...

  • Normalized Ricci flow on nonparabolic surfaces. Hao Yin // Annals of Global Analysis & Geometry;Aug2009, Vol. 36 Issue 1, p81 

    This paper studies the normalized Ricci flow on a nonparabolic surface, whose scalar curvature is asymptotically �1 in an integral sense. By a method initiated by R. Hamilton, the flow is shown to converge to a metric of constant scalar curvature �1. A relative estimate of Green�s...

  • Convergence of Kähler-Ricci Flow on Lower-Dimensional Algebraic Manifolds of General Type. Gang Tian; Zhenlei Zhang // IMRN: International Mathematics Research Notices;2016, Vol. 2016 Issue 21, p6493 

    In this paper, we prove that the L4-norm of Ricci curvature is uniformly bounded along a Kähler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold M of general type and with dimension n≤3, any solution of the normalized...

  • A pinching estimate for solutions of the linearized Ricci flow system on 3-manifolds. Anderson, Greg; Chow, Bennett // Calculus of Variations & Partial Differential Equations;May2005, Vol. 23 Issue 1, p1 

    The article presents information on apriori estimate for arbitrary solutions to the linearized Ricci flow on compact 3-manifolds which may be useful in its study. An important component of Hamilton's program for the Ricci flow on compact 3-manifolds is the classification of singularities which...

  • A simple proof on the non-existence of shrinking breathers for the Ricci flow. Hsu, Shu-Yu // Calculus of Variations & Partial Differential Equations;Sep2006, Vol. 27 Issue 1, p59 

    Suppose M is a compact n-dimensional manifold, n= 2, with a metric g ij ( x, t) that evolves by the Ricci flow ? t g ij = -2 R ij in M� (0, T). We will give a simple proof of a recent result of Perelman on the non-existence of shrinking breather without using the logarithmic Sobolev...

  • ON WEAKLY SYMMETRIC (LCS)n-MANIFOLD. Shaikh, Absos Ali; Binh, Tran Quoc // Journal of Advanced Mathematical Studies;Sep2009, Vol. 2 Issue 2, p103 

    The object of the present paper is to provide the existence of weakly symmetric and weakly Ricci-symmetric (LCS)n-manifolds by several non-trivial new examples and obtained various interesting results in such manifolds.

  • On the general structure of Ricci collineations for type B warped space–times. Flores, J. L.; Parra, Y.; Percoco, U. // Journal of Mathematical Physics;Sep2004, Vol. 45 Issue 9, p3546 

    A complete study of the structure of Ricci collineations for type B warped space–times is carried out. This study can be used as a method to obtain these symmetries in such space–times. Special cases as 2+2 reducible space–times, and plane and spherical symmetric...

  • The modeling of degenerate neck pinch singularities in Ricci flow by Bryant solitons. Garfinkle, David; Isenberg, James // Journal of Mathematical Physics;Jul2008, Vol. 49 Issue 7, p073505 

    In earlier work, carrying out numerical simulations of the Ricci flows of families of rotationally symmetric geometries on S3, we have found strong support for the contention that (at least in the rotationally symmetric case) the Ricci flow for a “critical” initial...

  • Some applications of Ricci flow in physics. Woolgar, E. // Canadian Journal of Physics;Apr2008, Vol. 86 Issue 4, p645 

    I discuss certain applications of the Ricci flow in physics. I first review how it arises in the renormalization group (RG) flow of a nonlinear sigma model. I then review the concept of a Ricci soliton and recall how a soliton was used to discuss the RG flow of mass in two dimensions. I then...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics