Evolution of hypersurfaces by powers of the scalar curvature

Alessandroni, Roberta; Sinestrari, Carlo

Alessandroni, Roberta ; Sinestrari, Carlo

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 3, pp. 541-571.

Résumé

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.

MR 2722655 | Zbl 1248.53047

Classification : 53C44, 35K55, 58J35, 35B40

@article{ASNSP_2010_5_9_3_541_0,
     author = {Alessandroni, Roberta and Sinestrari, Carlo},
     title = {Evolution of hypersurfaces by powers of the scalar curvature},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {541--571},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 9},
     number = {3},
     year = {2010},
     zbl = {1248.53047},
     mrnumber = {2722655},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2010_5_9_3_541_0/}
}

Alessandroni, Roberta; Sinestrari, Carlo. Evolution of hypersurfaces by powers of the scalar curvature. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 3, pp. 541-571. http://www.numdam.org/item/ASNSP_2010_5_9_3_541_0/

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