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Title in Portuguese: Complete submanifolds of Rn with finite topology
Author: Bessa, Gregório Pacelli Feitosa
Jorge, Luquésio Petrola de Melo
Montenegro, José Fábio Bezerra
Keywords: Superfícies mínimas
Issue Date: 2007
Citation: BESSA, Gregório Pacelli Feitosa ;JORGE, Luquésio Petrola de Melo ; MONTENEGRO, José Fábio Bezerra. Complete submanifolds of Rn with finite topology. Communications in Analysis and Geometry, v. 15, p. 725-732, 2007.
Abstract: We show that a complete m-dimensional immersed submanifold M of Rn with a(M) < 1 is properly immersed and have finite topology, where a(M) ⊂ [0,∞] is a scaling invariant number that gives the rate that the norm of the second fundamental form decays to zero at infinity. The class of submanifolds M ⊂ Rn with a(M) < 1 contains all complete minimal surfaces with finite total curvature, all m-dimensional minimal submanifolds with finite total scalar curvature ∫M|α|m dV < ∞ and all complete 2-dimensional surfaces with ∫M|α|2 dV < ∞ and non-positive curvature with respect to every normal direction.
metadata.dc.type: Artigo de Periódico
Appears in Collections:DMAT - Artigos publicados em revista científica

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