Closed weingarten hypersurfaces in riemannian manifolds

Journal of Differential Geometry

Volumn 43, Issue 3, 1996, Pages 612-641

  Gerhardt, Claus ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000239280     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214458325     Document Type: Article

References (14)

1. I. Bakelman & B. Kantor, Existence of spherically homeomorphic hypersurfaces in Euclidean space with prescribed mean curvature, Geometry and Topology, Leningrad, 1 (1974) 3-10.
2. L. Caffarelli, L. Nirenberg & J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian, Acta Math. 155 (1985) 261-301.
3. L. Caffarelli, L. Nirenberg & J. Spruck, Nonlinear second order elliptic equations IV: Starshaped compact Weingarten hyper surf aces, Current topics in partial differential equations. Y. Ohya, K. Kasahara & N. Shimakura (eds.), Kinokunize, Tokyo, 1985.
4. n+1 a courbure de Gauss positive prescrite, Ann. Sei. École Norm. Sup. (4) 18 (1985), 635-649.
5. M. P. Do Carmo & F. W. Warner, Rigidity and convexity of hypersurfaces in spheres, J. Differential Geom. 4 (1970) 133-144.
6. K. Ecker & G. Huisken, Immersed hypersurfaces with constant Weingarten curvature, Math. Ann. 283 (1989) 329-332.
7. C. Gerhardt, Flow of nonconvex hypersurfaces into spheres, J. Differential Geom. 32 (1990) 299-314.
8. C. Gerhardt, Closed Weingarten hypersurfaces in space forms, Preprint.
9. D. Gromoll, W. Klingenberg & W. Meyer, Riemannsche Geometrie im Großen, Lecture Notes in Math., Vol. 55, Springer, Berlin, 1975.
10. N. V. Krylov, Nonlinear elliptic and parabolic equations of second order, Reidel, Dordrecht, 1987.
11. D. S. Mitrinovic, Analytic inequalities, Springer, Berlin, 1970.
12. n+1 with prescribed Gaussian curvature and related equations of Monge-Ampere type, Comm. Partial Differential Equations 9 (1984) 807-838.
13. A. E. Treibergs & S. W. Wei, Embedded hypersurfaces with prescribed mean curvature, J. Differential Geom. 18 (1983) 513-521.
14. J. I. E. Urbas, On the expansion of convex hypersurfaces by symmetric functions of their principal radii of curvature, J. Differential Geom. 33 (1991) 91-125.