A convergence result for the Gradient Flow of ∫ |A|²in Riemannian Manifolds

• Autorzy: Annibale Magni
• Języki publikacji: EN

Abstrakty

EN

We study the gradient flow of the L2−norm of the second fundamental form for smooth immersions of two-dimensional surfaces into compact Riemannian manifolds. By analogy with the results obtained in [10] and [11] for the Willmore flow, we prove lifespan estimates in terms of the L2−concentration of the second fundamental form of the initial data and we show the existence of blowup limits. Under special condition both on the initial data and on the target manifold, we prove a long time existence result for the flow and the subconvergence to a critical immersion.

Słowa kluczowe

EN

Higher order geometric flows; Willmore functional; geometric measure theory

Kategorie tematyczne

• 49Q20: Variational problems in a geometric measure-theoretic setting
• 35K46: Initial value problems for higher-order parabolic systems
• 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

2014-05-08

zaakceptowano

2014-11-05

online

2015-01-10

Twórcy

autor

Annibale Magni

• Institut für Angewandte Mathematik, Westfälische–Wilhelms Universität Münster,
  Einsteinstrasse 62, 48149 Münster, Germany

Bibliografia

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Identyfikatory

DOI

10.1515/geofl-2015-0001