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Nous étudions des analogues en dimension supérieure de l’inégalité de Burago , avec une surface fermée de classe immergée dans , son
aire et sa courbure totale. Nous donnons un exemple explicite qui prouve qu’une
inégalité analogue de la forme , avec une
constante, ne peut être vraie pour une hypersurface fermée de classe dans
, . Nous mettons toutefois en évidence une condition suffisante
sur la courbure de Ricci sous laquelle l’inégalité est vérifiée en dimension . En
dimension...
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