We study geometric properties of complete non-compact bounded self-shrinkers and obtain natural restrictions that force these hypersurfaces to be compact. Furthermore, we observe that, to a certain extent, complete self-shrinkers intersect transversally a hyperplane through the origin. When such an intersection is compact, we deduce spectral information on the natural drifted Laplacian associated to the self-shrinker. These results go in the direction of verifying the validity of a conjecture by H.D. Cao concerning the polynomial volume growth of complete self-shrinkers. A finite strong maximum principle in case the self-shrinker is confined into a cylindrical product is also presented

Pigola, S., Rimoldi, M. (2013). Complete self-shrinkers confined into some regions of the space. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 45(1), 47-65 [10.1007/s10455-013-9387-8].

Complete self-shrinkers confined into some regions of the space

Pigola, S;RIMOLDI, MICHELE
2013

Abstract

We study geometric properties of complete non-compact bounded self-shrinkers and obtain natural restrictions that force these hypersurfaces to be compact. Furthermore, we observe that, to a certain extent, complete self-shrinkers intersect transversally a hyperplane through the origin. When such an intersection is compact, we deduce spectral information on the natural drifted Laplacian associated to the self-shrinker. These results go in the direction of verifying the validity of a conjecture by H.D. Cao concerning the polynomial volume growth of complete self-shrinkers. A finite strong maximum principle in case the self-shrinker is confined into a cylindrical product is also presented
Articolo in rivista - Articolo scientifico
Bounded self-shrinkers · Hyperplane intersection · Weighted manifolds ·Drifted Laplacian
English
2013
45
1
47
65
none
Pigola, S., Rimoldi, M. (2013). Complete self-shrinkers confined into some regions of the space. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 45(1), 47-65 [10.1007/s10455-013-9387-8].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/64595
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