Preface ......................................................... v
Moduli of continuity, isoperimetric profiles, and multi-point
estimates in geometric heat equations
Ben Andrews .................................................. 1
Rigidity and minimizing properties of quasi-local mass
Po-Ning Chen and Mu-Tao Wang ................................ 49
Lojasiewicz inequalities and applications
Tobias Holck Colding and William P. Minicozzi II ............ 63
The regularity of solutions in degenerate geometric problems
Panagiota Daskalopoulos ..................................... 83
Algebraic families of constant scalar curvature Kähler
metrics
Simon Donaldson ............................................ 111
Hermitian-Yang-Mills connections and beyond
Jun Li ..................................................... 139
Interior a priori estimates for the Monge-Ampиre equation
Jiakun Liu and Xu-Jia Wang ................................. 151
Dispersive geometric curve flows
Chuu-Lian Terng ............................................ 179
Regularity of stable minimal hypersurfaces: recent advances
in the theory and applications
Neshan Wickramasekera ...................................... 231
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