Main reference:

[1] Ecker, Klaus. Regularity theory for mean curvature flow. Progress in Nonlinear Differential Equations and their Applications, 57. Birkhäuser Boston, Inc., Boston, MA, 2004. xiv+165 pp. [MathSciNet]

Main reference:

[1] Giga, Yoshikazu. Surface evolution equations. A level set approach. Monographs in Mathematics, 99. Birkhäuser Verlag, Basel, 2006. xii+264 pp. [MathSciNet]

References related to exercises:

[2] Giga, Mi-Ho; Giga, Yoshikazu. Evolving graphs by singular weighted curvature. Arch. Rational Mech. Anal. 141 (1998), no. 2, 117–198. [MathSciNet]

[3] Giga, Mi-Ho; Giga, Yoshikazu. Generalized motion by nonlocal curvature in the plane. Arch. Ration. Mech. Anal. 159 (2001), no. 4, 295–333. [MathSciNet]

Additional reference related to exercises:

[4] Giga, Yoshikazu. Viscosity solutions with shocks. Comm. Pure Appl. Math. 55 (2002), no. 4, 431–480. [MathSciNet]

Exercises:

[5] Surface Evolution Equations – A level set approach. [Exercise sheet]

Main references:

[1] Grunau, Hans-Christoph; Sweers, Guido. Regions of positivity for polyharmonic Green functions in arbitrary domains. Proc. Amer. Math. Soc. 135 (2007), no. 11, 3537–3546. [MathSciNet] [Proceedings of AMS] [Preprint version]

[2] Grunau, Hans-Christoph; Robert, Frédéric. Positivity issues of biharmonic Green's functions under Dirichlet boundary conditions, preprint (2007/08). [arXiv] [Preprint]

[3] Dall'Acqua, Anna; Deckelnick, Klaus; Grunau, Hans-Christoph. Rotationally symmetric classical solutions of the Dirichlet problem for Willmore surfaces, preprint (2007). [Preprint]

[1] On the infinity Laplace operator [Presentation]