Lectures on Lipschitz analysis

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Local structure learning in high resolution remote sensing image retrieval (2016, background): “First, a lipschitz smooth function [11] is introduced to map the original space to a high-dimensional space.”
Differentiability of Intrinsic Lipschitz Functions within Heisenberg Groups (2011, methodology): “, [6, 16, 23, 24, 36, 37]).”
Private Empirical Risk Minimization, Revisited (2014, methodology): “We use the same extension in the proof McShane-Whitney theorem [21].”
Local Currents in Metric Spaces (2011, background): “In this context we just mention the functions of bounded higher variation [8, 9, 21, 24, 27], the recent progress on (generalized) flat chains [1, 18, 36, 37], the scans from [10, 11, 16], the differentiation theory on metric measure spaces [4, 5, 22], and the derivations from [29, 30].”
On quasiconformal self-mappings of the unit disk satisfying Poisson’s equation (2011, unknown): “Lemma 2.1. Let w be a harmonic function defined on the unit disk and assume that its derivative v = rw is bounded on the unit disk (or equivalently, according to Rademacher’s theorem [ 7 ], let w be Lipschitz continuous).”
Exactly Computing the Local Lipschitz Constant of ReLU Networks (2020, background): “• (Rademacher’s Theorem): If f is Lipschitz continuous, then f is differentiable everywhere except for a set of measure zero, under the standard Lebesgue measure in R n (Heinonen, 2005).”