Asymptotically Extrinsic Tamed Submanifolds

Abstract

ABSTRACT. 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 the so-called tamed immersions to obtain a description at infinity of the submanifold in the line of the structural results in [14] and [26] 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.