We study the evolution of a closed hypersurface of the euclidean space by a flow whose speed is given by a power of the scalar curvature. We prove that, if the initial shape is convex and satisfies a suitable pinching condition, the solution shrinks to a point in finite time and converges to a sphere after rescaling. We also give an example of a nonconvex hypersurface which develops a neckpinch singularity.
Alessandroni, R., Sinestrari, C. (2010). Evolution of hypersurfaces by powers of the scalar curvature. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 9, 541-571 [10.2422/2036-2145.2010.3.05].
Evolution of hypersurfaces by powers of the scalar curvature
SINESTRARI, CARLO
2010-01-01
Abstract
We study the evolution of a closed hypersurface of the euclidean space by a flow whose speed is given by a power of the scalar curvature. We prove that, if the initial shape is convex and satisfies a suitable pinching condition, the solution shrinks to a point in finite time and converges to a sphere after rescaling. We also give an example of a nonconvex hypersurface which develops a neckpinch singularity.File in questo prodotto:
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