Star-shaped p-convex hypersurfaces with prescribed curvature in space forms

Star-shaped p-convex hypersurfaces with prescribed curvature in space forms

In this paper, we establish curvature estimates for p-convex hypersurfaces with prescribed curvature for n2≤p≤n−1 in space forms Nn+1(K) with K=−1,0,1. Then the existence of a closed star-shaped p-convex hypersurface with prescribed curvature is obtained by the method of continuity.

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Veröffentlicht in:Journal of mathematical analysis and applications 2024-12, Vol.540 (2), p.128615, Article 128615
Hauptverfasser: Lu, Yueming, Zhong, Shuhui
Format: Artikel
Sprache:eng
Schlagworte:
Curvature estimates
p-convex hypersurfaces
Space forms
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Zusammenfassung:In this paper, we establish curvature estimates for p-convex hypersurfaces with prescribed curvature for n2≤p≤n−1 in space forms Nn+1(K) with K=−1,0,1. Then the existence of a closed star-shaped p-convex hypersurface with prescribed curvature is obtained by the method of continuity.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128615