From holomorphic functions to complex manifolds

By Klaus Fritzsche, H. Grauert. 2002

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A Course on Large Deviations With an Introduction to Gibbs Measures (2015, background): “Hint: Use the analytic implicit function theorem (page 34 of [37]) to show that the magnetization m(β, h) is analytic when h 6= 0 or β < 1/J .”
KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES (2014, unknown): “5 in Chapter VI of [FG02]) implies that Qa(τ,X) splits completely into linear factors for all a ∈W .”
PROPERTIES OF SQUEEZING FUNCTIONS AND GLOBAL TRANSFORMATIONS OF BOUNDED DOMAINS (2013, background): “lies det(df(z)) 6= 0. So the injectivity of f follows from Lemma 2.3 in [5] and the generalized Rouch´e’s theorem (Theorem 3 in [15]). Since f is injective, it is an open map (see e.g. Theorem 8.5 in [9]). On the other hand, it is clear that f(D) ⊂ Bn. So we have f(D) ⊂ Bn. We now provethat sD(z) ≥ ”