Curvature flow in hyperbolic spaces

References

[1] R. Alessandroni and C. Sinestrari, Evolution of hypersurfaces by powers of the scalar curvature, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9 (2010), no. 3, 541–571. 10.2422/2036-2145.2010.3.05Search in Google Scholar

[2] B. Andrews, Contraction of convex hypersurfaces in Euclidean space, Calc. Var. Partial Differential Equations 2 (1994), no. 2, 151–171. 10.1007/BF01191340Search in Google Scholar

[3] B. Andrews, Contraction of convex hypersurfaces in Riemannian spaces, J. Differential Geom. 39 (1994), no. 2, 407–431. 10.4310/jdg/1214454878Search in Google Scholar

[4] B. Andrews, Gauss curvature flow: The fate of the rolling stones, Invent. Math. 138 (1999), no. 1, 151–161. 10.1007/s002220050344Search in Google Scholar

[5] B. Andrews, Positively curved surfaces in the three-sphere, Proceedings of the international congress of mathematicians, ICM 2002. Vol. II: Invited lectures (Beijing 2002), Higher Education Press, Beijing (2002), 221–230. Search in Google Scholar

[6] B. Andrews, Fully nonlinear parabolic equations in two space variables, preprint (2004), http://arxiv.org/abs/math/0402235. Search in Google Scholar

[7] B. Andrews, Pinching estimates and motion of hypersurfaces by curvature functions, J. reine angew. Math. 608 (2007), 17–33. 10.1515/CRELLE.2007.051Search in Google Scholar

[8] B. Andrews, Moving surfaces by non-concave curvature functions, Calc. Var. Partial Differential Equations 39 (2010), no. 3–4, 649–657. 10.1007/s00526-010-0329-zSearch in Google Scholar

[9] B. Andrews and C. Baker, Mean curvature flow of pinched submanifolds to spheres, J. Differential Geom. 85 (2010), no. 3, 357–395. 10.4310/jdg/1292940688Search in Google Scholar

[10] B. Andrews and X. Chen, Surfaces moving by powers of Gauss curvature, Pure Appl. Math. Q. 8 (2012), no. 4, 825–834. 10.4310/PAMQ.2012.v8.n4.a1Search in Google Scholar

[11] B. Andrews and C. Hopper, The Ricci flow in Riemannian geometry, Lecture Notes in Math. 2011, Springer, Heidelberg 2011. 10.1007/978-3-642-16286-2Search in Google Scholar

[12] B. Andrews and J. McCoy, Convex hypersurfaces with pinched principal curvatures and flow of convex hypersurfaces by high powers of curvature, Trans. Amer. Math. Soc. 364 (2012), no. 7, 3427–3447. 10.1090/S0002-9947-2012-05375-XSearch in Google Scholar

[13] C. Baker, The mean curvature flow of submanifolds of high codimension, Ph.D. thesis, The Australian National University, 2010, http://arxiv.org/abs/1104.4409. Search in Google Scholar

[14] E. Cabezas-Rivas and V. Miquel, Volume preserving mean curvature flow in hyperbolic space, preprint (2006), http://arxiv.org/abs/math/0611216. 10.1512/iumj.2007.56.3060Search in Google Scholar

[15] B. Chow, Deforming convex hypersurfaces by the nth root of the Gaussian curvature, J. Differential Geom. 22 (1985), no. 1, 117–138. 10.4310/jdg/1214439724Search in Google Scholar

[16] B. Chow, Deforming convex hypersurfaces by the square root of the scalar curvature, Invent. Math. 87 (1987), no. 1, 63–82. 10.1007/BF01389153Search in Google Scholar

[17] E. DiBenedetto and A. Friedman, Hölder estimates for nonlinear degenerate parabolic systems, J. reine angew. Math. 357 (1985), 1–22. 10.1515/crll.1985.357.1Search in Google Scholar

[18] K. Ecker and G. Huisken, Interior estimates for hypersurfaces moving by mean curvature, Invent. Math. 105 (1991), no. 3, 547–569. 10.1007/BF01232278Search in Google Scholar

[19] R. S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), no. 2, 153–179. 10.4310/jdg/1214440433Search in Google Scholar

[20] R. S. Hamilton, Convex hypersurfaces with pinched second fundamental form, Commun. Anal. Geom. 2 (1994), no. 1, 167–172. 10.4310/CAG.1994.v2.n1.a10Search in Google Scholar

[21] G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geom. 20 (1984), no. 1, 237–266. 10.4310/jdg/1214438998Search in Google Scholar

[22] G. Huisken, Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature, Invent. Math. 84 (1986), no. 3, 463–480. 10.1007/BF01388742Search in Google Scholar

[23] G. Huisken, Deforming hypersurfaces of the sphere by their mean curvature, Math. Z. 195 (1987), 205–219. 10.1007/BF01166458Search in Google Scholar

[24] G. Huisken and A. Polden, Geometric evolution equations for hypersurfaces, Calculus of variations and geometric evolution problems. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) (Cetraro 1996), Lecture Notes Math. 1713, Springer, Berlin (1999), 45–84. 10.1007/BFb0092669Search in Google Scholar

[25] Q.-R. Li, Surfaces expanding by the power of the Gauss curvature flow, Proc. Amer. Math. Soc. 138 (2010), no. 11, 4089–4102. 10.1090/S0002-9939-2010-10431-8Search in Google Scholar

[26] O. C. Schnürer, Surfaces contracting with speed |A|2, J. Differential Geom. 71 (2005), no. 3, 347–363. 10.4310/jdg/1143571987Search in Google Scholar

[27] O. C. Schnürer, Surfaces expanding by the inverse Gauß curvature flow, J. reine angew. Math. 600 (2006), 117–134. 10.1515/CRELLE.2006.088Search in Google Scholar

[28] F. Schulze, Convexity estimates for flows by powers of the mean curvature, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 5 (2006), no. 2, 261–277. 10.2422/2036-2145.2006.2.06Search in Google Scholar

[29] K. Tso, Deforming a hypersurface by its Gauss–Kronecker curvature, Comm. Pure Appl. Math. 38 (1985), no. 6, 867–882. 10.1002/cpa.3160380615Search in Google Scholar

[30] C. Wu, D. Tian and G. Li, Forced flow by powers of the mth mean curvature, Armen. J. Math. 3 (2010), no. 2, 61–91. Search in Google Scholar