Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)

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The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$ (2016, neutral): “Theorem E (Kenig-Jerison extension, [1] Theorem 5.”
Reconstruction of Coefficients in Scalar Second‐Order Elliptic Equations from Knowledge of Their Solutions (2011, background): “Then there is a diffeomorphism φ from C → C, unique after normalization at infinity, such that [3] Dφ(z)J(z, φ(z))Dφ(z) = G(z).”
Lectures on Mappings of Finite Distortion (2014, background): “It is possible to show the existence of solutions under weaker assumptions (see [1] for exact statement and proofs), like for those compactly supported μ with exp( p 1−|μ(z)|) integrable for some p; this corresponds to the class of mappings whose distortion is not necessarily bounded but exp(λKf(x))”
Deformations of Annuli with Smallest Mean Distortion (2010, background): “A comprehensive overview of the theory of mappings of finite distortion in two-dimensions can be found in [3,14].”