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On the Moser-Onofri and Prékopa-Leindler inequalities.

Alessandro Ghigi — 2005

Collectanea Mathematica

Using elementary convexity arguments involving the Legendre transformation and the Prékopa-Leindler inequality, we prove the sharp Moser-Onofri inequality, which says that 1/16π ∫|∇φ|2 + 1/4π ∫ φ - log (1/4π ∫ eφ) ≥ 0 for any funcion φ ∈ C(S2).

On the approximation of functions on a Hodge manifold

Alessandro Ghigi — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

If ( M , ω ) is a Hodge manifold and f C ( M , ) we construct a canonical sequence of functions f N such that f N f in the C topology. These functions have a simple geometric interpretation in terms of the moment map and they are real algebraic, in the sense that they are regular functions when M is regarded as a real algebraic variety. The definition of f N is inspired by Berezin-Toeplitz quantization and by ideas of Donaldson. The proof follows quickly from known results of Fine, Liu and Ma.

Symmetries and Kähler-Einstein metrics

Claudio ArezzoAlessandro Ghigi — 2005

Bollettino dell'Unione Matematica Italiana

We consider Fano manifolds M that admit a collection of finite automorphism groups G 1 , ... , G k , such that the quotients M / G i are smooth Fano manifolds possessing a Kähler-Einstein metric. Under some numerical and smoothness assumptions on the ramification divisors, we prove that M admits a Kähler-Einstein metric too.

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