Course bibliography (2013-2014)- Alex Freire

A. BOOKS

K. Ecker, Regularity Theory for MCF, Birkhauser 2004

3. Local estimates via maximum principle/ 4. Integral estimates and monotonicity/ 5. Regularity at the first singular time

C. Mantegazza, Lectures on MCF, Birkhauser 2011

2. Evolution of geometric quantities/ 3. Monotonicity and type I singularities/ 4. Type II singularities

Survey: B. White Evolution of curves and surfaces by mean curvature, ICM 2002

B. RESEARCH PAPERS

1.1 Classic (differential geometry)

G. Huisken Flow by MC of convex surfaces into spheres, JDG 1984

K. Ecker, G.Huisken Mean curvature evolution of entire graphs, Annals 1989

K. Ecker, G. Huisken Interior estimates for hypersurfaces moving by MC, Inventiones 1991

G. Huisken, Asymptotic behavior of singularities for MCF, JDG 1990

B. Andrews, Contraction of convex hypersurfaces in Euclidean space, CV&PDE 1994

R. Hamilton, Harnack estimate for MCF, JDG 1995

J. Velazquez, Curvature Blow-up in perturbations of minimal cones evolving by MCF, Annali Pisa 1994

S. Angenent, J. Velazquez, Degenerate neck-pinches in MCF, J. Reine u. Angewandte Math 1997

1.2 Classic (weak solutions)

L.C. Evans, J. Spruck, Motion of Level Sets by MC (I), JDG 1991

YG Chen, Y.Giga, S.Goto, Uniqueness & Existence of Viscosity solutions for generalized MCF, JDG 1991

LC Evans, HM Soner, PE Souganidis Phase Transitions and generalized MCF, CPAM 1992

T. Ilmanen, Generalized flow of sets by MC on a manifold, Indiana U Math. J 1992

HM Soner, Motion of a set by the curvature of its boundary, JDE 1993

T. Ilmanen, Convergence of the Allen-Cahn equation to Brakke's motion by MC, JDG 1993

T. Ilmanen, Elliptic regularization and partial regularity for motion by MC, Memoirs AMS 1993

S. Altschuler, S. Angenent, Y. Giga, MCF through singularities for surfaces of Revolution, J. Geom. Analysis 1995

2.1 Semi-modern

G. Huisken, C. Sinestrari, MCF singularities for mean-convex surfaces, CV&PDE 1999

K. Smoczyk, Starshaped hypersurfaces and MCF, Manuscripta 1998

G. Huisken, C. Sinestrari, Convexity estimates for MCF and singularities of mean-convex surfaces, Acta Math. 1999

B. White, The size of the singular set in MCF of mean-convex sets, JAMS 2000

B. White, The nature of singularities in MCF of mean-convex sets, JAMS 2003

B White, A local regularity theorem for MCF, Annals 2005

2.2 Inverse mean curvature flow

J. Urbas, Expansion of starshaped hypersurfaces by symmetric functions of principal curvatures, Math Z. 1990

C. Gerhardt, Flow of nonconvex hypersurfaces into spheres, JDG 1990

B. Chow, R. Gulliver, Aleksandrov reflection and geometric evolution of hypersurfaces, CA&G 2001

P. Guan, J. Li, Quermassintegral inequalities for starshaped domains, Arxiv (2007)

G. Huisken, T. Ilmanen, The IMCF and the Riemannian Penrose inequality, JDG 2001

G. Huisken, T. Ilmanen, Higher Regularity of the IMCF, JDG 2008

2.3 Recent

G. Huisken, C. Sinestrari, MCF with surgeries for 2-convex hypersurfaces, Inventiones 2009

B. Andrews, Non-collapsing in mean-convex MCF, Arxiv 2011

XJ Wang, Convex solutions to the MCF, Annals 2011

B. White, Subsequent singularities in MCF, ArXiv 2011, 2013

TH Colding, WP Minicozzi, Generic MCF(I): generic singularities, Annals 2012

R. Haslhofer, B. Kleiner, MCF of mean-convex hypersurfaces, ArXiv (2013)

S. Brendle, Sharp bound for the inscribed radius under MCF, ArXiv (2013)

S. Brendle, G. Huisken, MCF with surgery of mean-convex surfaces in R3, ArXiv (2013)

TH Colding, WP Minicozzi, Rigidity of generic singularities of MCF, ArXiv (2013)

TH Colding, WP Minicozzi, Uniqueness of blowups and Lojasiewicz inequalities, ArXiv (2013)

B. Andrews, M. Langford, Two-sided non-collapsing curvature flows, ArXiv 2013/2014