Hypersurfaces with constant mean curvature in a real space form

Шу, Шичанг; Liu, Sanyang

doi:10.3906/mat-0904-59

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Uniqueness Of Spacelike Hypersurfaces With Prescribed Curvat...2

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2021

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“…We will focus on general elliptic Weingaten hypersurfaces when n 3. Different results are known in this case for the rth mean curvatures and for some linear Weingarten functionals (see [3,8,17,25,35,37,38,40,41,46,51,52] and references therein).…”

Section: Uniqueness Of Spacelike Hypersurfaces With Prescribed Curvat...mentioning

confidence: 99%

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Hypersurfaces with prescribed curvatures in the de Sitter space

Roldán

2021

Rev. Mat. Iberoam.

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In this paper, we establish a relationship between spacelike hypersurfaces in the de Sitter space S nC1 1 and conformal metrics on the sphere S n . As a consequence of this relation and some deep results in conformal geometry, we classify spacelike hypersurfaces in S nC1 1 satisfying certain global conditions and a very general Weingarten relation W .k 1 ; : : : ; k n / D 0 of elliptic type, where k 1 ; : : : ; k n are its principal curvatures. Also, we particularize to some important cases as the rth mean curvatures.

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Section: Uniqueness Of Spacelike Hypersurfaces With Prescribed Curvat...mentioning

confidence: 99%

“…The additional hypothesis in Theorem 4.4 are necessary to ensure that the immersion is totally umbilical, since there are non totally umbilical complete Weingarten hypersurfaces for many different functionals (see, for instance, [25,37,38,46]).…”

Section: Uniqueness Of Spacelike Hypersurfaces With Prescribed Curvat...mentioning

confidence: 99%

Hypersurfaces with prescribed curvatures in the de Sitter space

Roldán

2021

Rev. Mat. Iberoam.

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Hypersurfaces with constant mean curvature in a real space form

Cited by 1 publication

References 6 publications

Hypersurfaces with prescribed curvatures in the de Sitter space

Hypersurfaces with prescribed curvatures in the de Sitter space

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