Régularité des cônes et d’ensembles minimaux de dimension 3 dans R4

Abstract : In this thesis we study the problems of regularity of three-dimensional minimal cones and sets in l'espace Euclidien de dimension 4In the first part we study the Hölder regularity for minimal cones of dimension 3 in l'espace Euclidien de dimension 4. Then we use this for showing that there exists a local diffeomorphic mapping between a minimal cone of dimension 3 and a minimal cone of dimension 3 of type P, Y or T, away from the origin. The techniques used here are the same as the ones for the regularity of two-dimensional minimal sets. We construct some competitors to reduce to the known situation of two-dimensional minimal sets in l'espace Euclidien de dimension 3.In the second part, we use the first part to give somme results of the Hölder regularity for three-dimensional minimal sets in l'espace Euclidien de dimension 4. We interested also in Mumford-Shah minimal sets and we get a result of the existence of a T-point.
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Tien Duc Luu. Régularité des cônes et d’ensembles minimaux de dimension 3 dans R4. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI, 2011. Français. ⟨NNT : 2011PA112301⟩. ⟨tel-00665664⟩

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