Some remarks on positive scalar and Gauss-Kronecker curvature hypersurfaces of ℝ n + 1 and ℍ n + 1

Barbara Nelli; Harold Rosenberg

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 4, page 1209-1218
  • ISSN: 0373-0956

Abstract

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We consider graphs of positive scalar or Gauss-Kronecker curvature over a punctured disk in Euclidean and hyperbolic n -dimensional space and we obtain removable singularities theorems.

How to cite

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Nelli, Barbara, and Rosenberg, Harold. "Some remarks on positive scalar and Gauss-Kronecker curvature hypersurfaces of ${\mathbb {R}}^{n+1}$ and ${\mathbb {H}}^{n+1}$." Annales de l'institut Fourier 47.4 (1997): 1209-1218. <http://eudml.org/doc/75260>.

@article{Nelli1997,
abstract = {We consider graphs of positive scalar or Gauss-Kronecker curvature over a punctured disk in Euclidean and hyperbolic $n$-dimensional space and we obtain removable singularities theorems.},
author = {Nelli, Barbara, Rosenberg, Harold},
journal = {Annales de l'institut Fourier},
keywords = {scalar curvature; isolated singularity; maximum principle; Gauss-Kronecker curvature},
language = {eng},
number = {4},
pages = {1209-1218},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some remarks on positive scalar and Gauss-Kronecker curvature hypersurfaces of $\{\mathbb \{R\}\}^\{n+1\}$ and $\{\mathbb \{H\}\}^\{n+1\}$},
url = {http://eudml.org/doc/75260},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Nelli, Barbara
AU - Rosenberg, Harold
TI - Some remarks on positive scalar and Gauss-Kronecker curvature hypersurfaces of ${\mathbb {R}}^{n+1}$ and ${\mathbb {H}}^{n+1}$
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 4
SP - 1209
EP - 1218
AB - We consider graphs of positive scalar or Gauss-Kronecker curvature over a punctured disk in Euclidean and hyperbolic $n$-dimensional space and we obtain removable singularities theorems.
LA - eng
KW - scalar curvature; isolated singularity; maximum principle; Gauss-Kronecker curvature
UR - http://eudml.org/doc/75260
ER -

References

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  1. [ACC] H. ALENCAR, M. DO CARMO, A.G. COLARES, Stable Hypersurfaces with Constant Scalar Curvature, Math. Z., 213 (1993), 117-131. Zbl0792.53057MR94d:53080
  2. [L] M.L. LEITE, Rotational Hypersurfaces of Space Forms with Constant Scalar Curvature, Manuscripta Math., 67 (1990), 285-304. Zbl0695.53040MR91d:53085
  3. [N] B. NELLI, Constant Curvature Hypersurfaces of Hyperbolic Space, PhD Thesis, Université de Paris VII, 1995. Zbl0831.53039
  4. [NSa] B. NELLI, R. SA EARP, Some Properties of Surfaces of Prescribed Mean Curvature in ℍn+1, Bull. Soc. Math., 6 (1996), 537-553. Zbl0872.53008MR97i:53006
  5. [NSe] B. NELLI, B. SEMMLER, Some Remarks on Compact Constant Mean Curvature Hypersurfaces in a Halfspace of ℍn+1, to appear in J. Geometry. Zbl0981.53049
  6. [NSp] B. NELLI, J. SPRUCK, Existence and Uniqueness of Mean Curvature Hypersurface, Preprint. Zbl0936.35069
  7. [R] H. ROSENBERG, Hypersurfaces of Constant Curvature in Space Forms, Bull. Soc. Math., 2e série, 117 (1993), 211-239. Zbl0787.53046MR94b:53097
  8. [RSa] H. ROSENBERG, R. SA EARP, Some Remarks on Surfaces of Prescribed Mean Curvature, Pitman Monographs and Surveys in Pure and Applied Mathematics 52 (1991), 123-148. Zbl0773.53002MR93k:53010
  9. [Sp] M. SPIVAK, A Comprehensive Introduction to Differential Geometry IV, Publish or Perish Inc., Berkley, 1979. Zbl0439.53004MR82g:53003d

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