References
- B. H. Andrews, Contraction of convex hypersurfaces in Euclidean space, Calc. Var. Partial Differential Equations 2 (1994), no. 2, 151-171. https://doi.org/10.1007/BF01191340
- B. H. Andrews, Contraction of convex hypersurfacs in Riemannian spaces, J. Differential Geom. 39 (1994), no. 2, 407-431. https://doi.org/10.4310/jdg/1214454878
- B. H. Andrews, Gauss curvature flow: the fate of the rolling stones, Invent. Math. 138 (1999), no. 1, 151-161. https://doi.org/10.1007/s002220050344
- B. H. Andrews, Motion of hypersurfaces by Gauss curvature, Pacific J. Math. 195 (2000), no. 1, 1-36. https://doi.org/10.2140/pjm.2000.195.1
- B. H. Andrews, Moving surfaces by non-concave curvature functions, preprint (2004), available at arXiv:math.DG/0402273.
- A. Borisenko and V. Miquel, Total curvatures of convex hypersurfaces in hyperbolic space, Illinois J. Math. 43 (1999), no. 1, 61-78.
- E. Cabezas-Rivas and V. Miquel, Volume preserving mean curvature flow in the hyperbolic space, Indiana Univ. Math. J. 56 (2007), no. 5, 2061-2086. https://doi.org/10.1512/iumj.2007.56.3060
- B. Chow, Deforming convex hypersurfaces by the nth root of the Gaussian curvature, J. Differential Geom. 22 (1985), no. 1, 117-138.
- B. Chow, Deforming convex hypersurfaces by the square root of the scalar curvature, Invent. Math. 87 (1987), no. 1, 63-82. https://doi.org/10.1007/BF01389153
- R. J. Currier, On hypersurfaces of hyperbolic space infinitesimally supported by horospheres, Trans. Amer. Math. Soc. 313 (1989), no. 1, 419-431. https://doi.org/10.1090/S0002-9947-1989-0935532-0
- R. E. Greene and H. Wu, Function Theory on Manifolds which possess a Pole, Springer Verlag, LNM 699, Berlin-Heidelberg-New York, 1979.
- R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), no. 2, 255-306.
- M. Heidusch, Zur Regularitat des Inversen Mittleren Krummungsfusses, PhD thesis, Eberhard-Karls-Universitat Tubingen, 2001.
- G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geom. 20 (1984), no. 1, 237-266. https://doi.org/10.4310/jdg/1214438998
- G. Huisken, Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature, Invent. Math. 84 (1986), no. 3, 463-480. https://doi.org/10.1007/BF01388742
- G. Huisken and C. Sinestrari, Convexity estimates for mean curvature flow and singularities of mean convex surfaces, Acta Math. 183 (1999), no. 1, 45-70. https://doi.org/10.1007/BF02392946
- G. Huisken and A. Polden, Geometric evolution equations for hypersurfaces, Calculus of variations and geometric evolution problems (Cetraro, 1996), 45-84, Lecture Notes in Math., 1713, Springer, Berlin, 1999.
- N. V. Krylov, Nonlinear Elliptic and Parabolic Equations of the Second Order, D. Reidel, 1978.
- G. Li, L. Yu, and C. Wu, Curvature flow with a general forcing term in Euclidean spaces, J. Math. Anal. Appl. 353 (2009), no. 2, 508-520. https://doi.org/10.1016/j.jmaa.2008.12.030
- G. M. Lieberman, Second Order Parabolic Differential Equations, World Scientific, 1996.
- J. A. McCoy, Mixed volume preserving curvature flows, Calc. Var. Partial Differential Equations. 24 (2005), no. 2, 131-154. https://doi.org/10.1007/s00526-004-0316-3
- P. Petersen, Riemannian Geometry. Springer Verlag, New York, 1998.
-
O. C. Schnurer, Surfaces contracting with speed
$|A|^2$ , J. Differential Geom. 71 (2005), no. 3, 347-363. https://doi.org/10.4310/jdg/1143571987 - F. Schulze, Evolution of convex hypersurfaces by powers of the mean curvature, Math. Z. 251 (2005), no. 4, 721-733. https://doi.org/10.1007/s00209-004-0721-5
- J. Simons, Minimal varieties in Riemannian manifolds, Ann. of Math. (2) 88 (1968), 62-105. https://doi.org/10.2307/1970556
- K. Tso, Deforming a hypersurface by its Gauss-Kronecker curvature, Comm. Pure Appl. Math. 38 (1985), no. 6, 867-882. https://doi.org/10.1002/cpa.3160380615
Cited by
- DEFORMING PINCHED HYPERSURFACES OF THE HYPERBOLIC SPACE BY POWERS OF THE MEAN CURVATURE INTO SPHERES vol.53, pp.4, 2016, https://doi.org/10.4134/JKMS.j140445
- Contracting Convex Hypersurfaces in Space Form by Non-homogeneous Curvature Function pp.1559-002X, 2019, https://doi.org/10.1007/s12220-019-00148-9