Details

Autor(en) / Beteiligte

• Chahine, Yousef K.

Titel

Volume Estimates for Tubes Around Submanifolds Using Integral Curvature Bounds

Ist Teil von

• The Journal of geometric analysis, 2020-12, Vol.30 (4), p.4071-4091

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2020

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We generalize an inequality of Heintze and Karcher (Ann Sci École Norm Sup 11(4):451–470, 1978) for the volume of tubes around minimal submanifolds to an inequality based on integral bounds for k -Ricci curvature. Even in the case of a pointwise bound, this generalizes the classical inequality by replacing a sectional curvature bound with a k -Ricci bound. This work is motivated by the estimates of Petersen–Shteingold–Wei (Geom Funct Anal 7(6):1011–1030, 1997) for the volume of tubes around a geodesic and generalizes their result. Using similar ideas we also prove a Hessian comparison theorem for k -Ricci curvature which generalizes the usual Hessian and Laplacian comparison for distance functions from a point and give several applications.