Analysis aspects of Willmore surfaces

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Variational Principles for immersed Surfaces with $L^2$-bounded Second Fundamental Form (2010, methodology): “One of the main computation in [18] establishes that in conformal coordinates ‰ from D(2) into Bri .”
The Willmore Conjecture (2014, background): “In [52], Rivière derives a general weak formulation of the Willmore Euler-Lagrange equation in divergence form, in any codimension, and proves regularity of weak solutions.”
Min-Max theory and the Willmore conjecture (2012, unknown): “, [34]).”
Energy quantization for Willmore surfaces and applications (2011, methodology): “For some ε 0 chosen smaller than the constant ε appearing in the ε -regularity Theorem I.5 in [Riv08], we apply Proposition III.1 so as to obtain a subsequence for which we can decompose the surface into “converging regions” (complements of small neighborhoods of the points a i ), bubbles, and neck…”