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Theses

Inégalités géométriques et fonctionnelles

Abstract : This thesis is mostly about the Blaschke-Santaló inequality, which states that among symmetric sets, the Euclidean ball maximises the product vol(K) vol(K°), where K° is the polar body of K. Several authors (Ball, Artstein, Klartag, Milman, Fradelizi, Meyer. . .) were able to derive functional inequalities from this inequality. The purpose of this thesis is to give direct proofs of these functional Santaló inequalities. This provides new proofs of Santaló, some of which are very simple. The last chapter is about Gaussian chaoses. We obtain a sharp bound for moments of Gaussian chaoses due to Lataªa, using the generic chaining of Talagrand
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Joseph Lehec. Inégalités géométriques et fonctionnelles. Mathématiques générales [math.GM]. Université Paris-Est, 2008. Français. ⟨NNT : 2008PEST0231⟩. ⟨tel-00365744v2⟩

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