A volume preserving flow and the isoperimetric problem in warped product spaces
In this article, we continue the work in [Int. Math. Res. Not.IMRN 13 (2015), pp. 4716-4740] and study a normalized hypersurface flow in the more general ambient setting of warped product spaces. This flow preserves the volume of the bounded domain enclosed by a graphical hypersurface and monotonica...
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| Veröffentlicht in: | Transactions of the American Mathematical Society 2019-08, Vol.372 (4), p.2777-2798 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this article, we continue the work in [Int. Math. Res. Not.IMRN 13 (2015), pp. 4716-4740] and study a normalized hypersurface flow in the more general ambient setting of warped product spaces. This flow preserves the volume of the bounded domain enclosed by a graphical hypersurface and monotonically decreases the hypersurface area. As an application, the isoperimetric problem in warped product spaces is solved for such domains. |
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| ISSN: | 0002-9947 1088-6850 |
| DOI: | 10.1090/tran/7661 |