MoserFlow: Divergence-basedGenerativeModeling onManifolds Supplementary NoamRozen1 AdityaGrover2,3 MaximilianNickel2 YaronLipman1,2 1WeizmannInstituteofScience 2FacebookAIResearch 3UCLA

We will review here the proof of Moser Theorem 1; for more details see Moser's original paper (Moser,1965)orLang(2012),Chapter18section2. First we show that µ = µ is a minimizer of the loss. Proposition 1.2 in Lang (2012) and Definition 1 in Section 4-4 in Do Carmo (2016) imply that for submanifolds with induced metric the Riemannian covariant derivative at Since M is compact, Ω is also compact. According to Theorem 1 there exists a vector fieldu? Note that the l.h.s. of this equation is a sum of Given atriangular surface meshM0, we wish to calculate thek-th eigenfunction of the (discrete) Laplace-Beltrami operator overM0.