Differential and Integral Equations

The Willmore flow near spheres

Gieri Simonett

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The Willmore flow leads to a quasilinear evolution equation of fourth order. We study existence, uniqueness and regularity of solutions. Moreover, we prove that solutions exist globally and converge exponentially fast to a sphere, provided that they are initially close to a sphere.

Article information

Differential Integral Equations, Volume 14, Number 8 (2001), 1005-1014.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 35K55: Nonlinear parabolic equations


Simonett, Gieri. The Willmore flow near spheres. Differential Integral Equations 14 (2001), no. 8, 1005--1014. https://projecteuclid.org/euclid.die/1356123177

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