Asymptotically Extrinsic Tamed Submanifolds

We study, from the extrinsic point of view, the structure at infinity of open submanifolds, φ : M m ↪ M n ( κ ) isometrically immersed in the real space forms of constant sectional curvature κ ≤ 0 . We shall use the decay of the second fundamental form of the so-called tamed immersions to obtain a d...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of geometric analysis 2018, Vol.28 (1), p.448-472
Main Authors: Bessa, G. Pacelli, Gimeno, Vicent, Palmer, Vicente
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Curvature
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Infinity
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study, from the extrinsic point of view, the structure at infinity of open submanifolds, φ : M m ↪ M n ( κ ) isometrically immersed in the real space forms of constant sectional curvature κ ≤ 0 . We shall use the decay of the second fundamental form of the so-called tamed immersions to obtain a description at infinity of the submanifold in the line of the structural results in Greene et al. (Int Math Res Not 1994:364–377, 1994 ) and Petrunin and Tuschmann (Math Ann 321:775–788, 2001 ) and an estimation from below of the number of its ends in terms of the volume growth of a special class of extrinsic domains, the extrinsic balls .
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-017-9828-x