BIBLIOGRAPHY ON MEAN CURVATURE FLOW AND RELATED TOPICS
(limited to what will be discussed in the course).
I. Books
Klaus Ecker, Regularity Theory for
Mean Curvature Flow (Birkhauser 2004)
Tom Ilmanen, Elliptic Regularization
and Partial Regularity for Motion by Mean Curvature (Memoirs AMS
vol. 108, no. 520, 1994)
II. Papers
a) Classical solutions
G. Huisken, Flow by mean curvature
of convex surfaces into spheres, JDG 20 (1984).
G.Huisken, Asymptotic behavior for
singularities of mean curvature flow, JDG 31 (1990).
K.Ecker, G. Huisken, Mean curvature
evolution of entire graphs, Annals 130 (1989)
K. Ecker, G. Huisken, Interior
estimates for hypersurfaces moving by mean curvature,
Inventiones 105 (1991)
K. Smoczyk, Starshaped hypersurfaces
and MCF, Manuscripta math, 95, 225-236
b) Weak solutions
L.C. Evans, J. Spruck, Motion of
Level Sets by Mean Curvature, JDG 33 (1991)
T. Ilmanen, Generalized Flow of Sets
by Mean Curvature on a Manifold, Indiana U Math J, 41 (1992)
c) Singularity formation
S. Altschuler, S. Angenent, Y.Giga, Mean
Curvature Flow through Singularities for Surfaces of Rotation,
J.Geom. Analysis 5 (1995)
S. Angenent, J. Velazquez, Degenerate
Neckpinches in MCF, Crelle 482 (1997)
d) MCF for mean-convex hypersurfaces
G. Huisken, C. Sinestrari, MCF
singularities for mean-convex surfaces, Calc. Variations &
PDE 8 (1999)
G. Huisken, C. Sinestrari, Convexity
estimates for MCF and singularities of mean-convex surfaces,
Acta 183 (1999)
B. White, The size of the singular
set in MCF of mean-convex sets, JAMS 13 (2000)
B. White, The nature of
singularities in MCF of mean-convex sets, JAMS 16 (2003) (see
also B. White's web page)
R. Haslhofer, B. Kleiner, MCF of mean-convex
hypersurfaces (arXiv, 2013)
e) Inverse mean curvature flow
G. Huisken, T. Ilmanen, The Inverse Mean Curvature Flow and the
Riemannian Penrose Inequality, JDG 59 (2001)
G.Huisken, T. Ilmanen, Higher Regularity of IMCF, JDG 80 (2008)
f) MCF with surgery
G. Huisken, C. Sinestrari, MCF with
surgeries for two-convex hypersurfaces, Inventiones 175 (2009)
S. Brendle, G. Huisken, MCF
with surgery of mean-convex surfaces in R^3, (arXiv, 2013)
S. Brendle, Sharp
estimate for the inscribed radius under MCF (arXiv, 2013)