Article PDF
Avoid common mistakes on your manuscript.
References
Andrews, B.H.: Contraction of convex hypersurfaces in Euclidean space. Calc. Var. 2(2), 151-171 (1994)
Andrews, B.H.: Contraction of convex hypersurfaces in Riemannian spaces. J. Differential Geometry 39, 407-431 (1994)
Andrews, B.H.: Volume-preserving anisotropic mean curvature flow. Indiana Univ. Math. J. 50(2), 783-827 (2001)
Andrews, B.H.: Pinching estimates and motion of hypersurfaces by curvature functions. (Preprint)
Andrews, B.H.: Fully nonlinear parabolic equations in two space variables. (Preprint)
Andrews, B.H.: Moving surfaces by non-concave curvature functions. (Preprint)
Caffarelli, L.A.: Interior a priori estimates for solutions of fully non-linear equations. Ann. Math. 130, 189-213 (1989)
Chow, B.: Deforming convex hypersurfaces by the nth root of the Gaussian curvature. J. Differential Geometry 22, 117-138 (1985)
Chow, B.: Deforming convex hypersurfaces by the square root of the scalar curvature. Invent. math. 87, 63-82 (1987)
Chow, B., Gulliver, R.: Aleksandrov reflection and geometric evolution equations I: The n-sphere and n-ball. Calc. Var. 4, 249-264 (1996)
Gage, M.: On an area-preserving evolution for planar curves. Contemp. Math. 51, 51-62 (1986)
Gage, M., Hamilton, R.S.: The heat equation shrinking convex plane curves. J. Differential Geom. 23, 69-96 (1986)
Gerhardt, C.: Flow of nonconvex hypersurfaces into spheres. J. Differential Geom. 32, 299-314 (1990)
Gerhardt, C.: Closed Weingarten hypersurfaces in Riemannian manifolds. J. Differential Geom. 43, 612-641 (1996)
Giga, Y., Goto, S.: Geometric evolution of phase boundaries. On the evolution of phase boundaries, IMA Volumes in Mathematics and its Applications 43. Springer, Berlin Heidelberg New York 1992
Gurtin, M.E., Jabbour, M.E.: Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: interface-controlled evolution, phase transitions, epitaxial growth of elastic films. Arch. Rational Mech. Anal. 163, 171-208 (2002)
Hamilton, R.S.: Three-manifolds with positive Ricci curvature. J. Differential Geometry 17, 255-306 (1982)
Hamilton, R.S.: Four-manifolds with positive curvature operator. J. Differential Geometry 24, 153-179 (1986)
Huisken, G.: Flow by mean curvature of convex surfaces into spheres. J. Differential Geometry 20, 237-266 (1984)
Huisken, G.: The volume preserving mean curvature flow. J. reine angew. Math. 382, 35-48 (1987)
Huisken, G.: Asymptotic behaviour for singularities of the mean curvature flow. J. Differential Geometry 31, 285-299 (1990)
Huisken, G., Polden, A.: Geometric evolution equations for hypersurfaces. Lecture Notes in Mathematics, 1713. Springer, Berlin Heidelberg New York 1999
Krylov, N.V., Safonov, M.V.: A certain property of solutions of parabolic equations with measurable coefficients. Izv. Akad. Nauk 40, 161-175 (1980). English transl., Math. USSR Izv. 16, 151-164 (1981)
Lieberman, G.M.: Second order parabolic differential equations. World Scientific, Singapore 1996
Lunardi, A.: Analytic semigroups and optimal regularity in parabolic problems. Birkhäuser, Basel 1995
McCoy, J.A.: The surface area preserving mean curvature flow. Asian J. Math. 7(1), 7-30 (2003)
McCoy, J.A.: The mixed volume preserving mean curvature flow. Math. Z. 246(1), 155-166 (2004)
Pihan, D.M.: A length preserving geometric heat flow for curves. PhD thesis, University of Melbourne (1998)
Tso, K.: Deforming a hypersurface by its Gauss-Kronecker curvature. Comm. Pure Appl. Math. 38, 867-882 (1985)
Urbas, J.I.E.: On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures. Math. Z. 205, 355-372 (1990)
Urbas, J.I.E.: An expansion of convex hypersurfaces. J. Differential Geometry 33, 91-125 (1991)
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 2 February 2004, Accepted: 19 October 2004, Published online: 22 December 2004
Rights and permissions
About this article
Cite this article
McCoy, J.A. Mixed volume preserving curvature flows. Calc. Var. 24, 131–154 (2005). https://doi.org/10.1007/s00526-004-0316-3
Issue Date:
DOI: https://doi.org/10.1007/s00526-004-0316-3