Asymptotically Tamed Submanifolds

Abstract: We study, from the extrinsic point of view, the structure at infinity of open submanifolds, $ϕ: M^m → M^n(\kappa)$ isometrically immersed in the real space forms of constant sectional curvature $κ ≤ 0$. We 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

This is a joint work with Vicent Gimeno & Vicente Palmer (J. Geom. Anal. 28 (2018), no. 1, 448–472.)

PortugueseMathematics

Audience: general audience

Seminários de Matemática da UFPB