Moving surfaces by non-concave curvature functions
Abstract
A convex surface contracting by a strictly monotone, homogeneous degree one function of curvature remains smooth until it contracts to a point in finite time, and is asymptotically spherical in shape. No assumptions are made on the concavity of the speed as a function of principal curvatures.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- February 2004
- DOI:
- arXiv:
- arXiv:math/0402273
- Bibcode:
- 2004math......2273A
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Analysis of PDEs;
- 53C44 (Primary) 35K55 (Secondary)
- E-Print:
- Extensively revised. Corrected expression for pinching ratio bound in Theorem 3. Additional details on smooth convergence in Section 5