Displaying similar documents to “Some evolution equations under the List's flow and their applications”

How to produce a Ricci flow via Cheeger–Gromoll exhaustion

Esther Cabezas-Rivas, Burkhard Wilking (2015)

Journal of the European Mathematical Society

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We prove short time existence for the Ricci flow on open manifolds of non-negative complex sectional curvature without requiring upper curvature bounds. By considering the doubling of convex sets contained in a Cheeger–Gromoll convex exhaustion and solving the singular initial value problem for the Ricci flow on these closed manifolds, we obtain a sequence of closed solutions of the Ricci flow with non-negative complex sectional curvature which subconverge to a Ricci flow on the open...

Introduction to mean curvature flow

Roberta Alessandroni (2008-2009)

Séminaire de théorie spectrale et géométrie

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This is a short overview on the most classical results on mean curvature flow as a flow of smooth hypersurfaces. First of all we define the mean curvature flow as a quasilinear parabolic equation and give some easy examples of evolution. Then we consider the M.C.F. on convex surfaces and sketch the proof of the convergence to a round point. Some interesting results on the M.C.F. for entire graphs are also mentioned. In particular when we consider the case of dimension one, we can compute...

Curvature cones and the Ricci flow.

Thomas Richard (2012-2014)

Séminaire de théorie spectrale et géométrie

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This survey reviews some facts about nonnegativity conditions on the curvature tensor of a Riemannian manifold which are preserved by the action of the Ricci flow. The text focuses on two main points. First we describe the known examples of preserved curvature conditions and how they have been used to derive geometric results, in particular sphere theorems. We then describe some recent results which give restrictions on general preserved conditions. ...

Curvature and Flow in Digital Space

Atsushi Imiya (2013)

Actes des rencontres du CIRM

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We first define the curvature indices of vertices of digital objects. Second, using these indices, we define the principal normal vectors of digital curves and surfaces. These definitions allow us to derive the Gauss-Bonnet theorem for digital objects. Third, we introduce curvature flow for isothetic polytopes defined in a digital space.