Evolution of convex entire graphs by curvature flows

• Autorzy: Roberta Alessandroni , Carlo Sinestrari
• Języki publikacji: EN

Abstrakty

EN

We consider the evolution of an entire convex graph in euclidean space with speed given by a symmetric function of the principal curvatures. Under suitable assumptions on the speed and on the initial data, we prove that the solution exists for all times and it remains a graph. In addition, after appropriate rescaling, it converges to a homothetically expanding solution of the flow. In this way, we extend to a class of nonlinear speeds the well known results of Ecker and Huisken for the mean curvature flow.

Kategorie tematyczne

• 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Geometric Flows
• Rocznik: 2015
• Tom: 1
• Numer: 1

Daty

otrzymano

2014-10-21

zaakceptowano

2015-04-20

online

2015-11-03

Twórcy

autor

Roberta Alessandroni

• Mathematisches Institut, Albert-Ludwigs-Universität Freiburg

autor

Carlo Sinestrari

• Dipartimento di Matematica, Università di Roma “Tor Vergata”

Bibliografia

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Identyfikatory

DOI

10.1515/geofl-2015-0006