(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)