Positivity of Curvature on Manifolds with Boundary

2020/12/01 by Chow, Tsz-Kiu Aaron · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.00255

Abstract

Consider a compact manifold M with smooth boundary ∂ M. Suppose that g and g are two Riemannian metrics on M. We construct a family of metrics on M which agrees with g outside a neighborhood of ∂ M and agrees with g in a neighborhood of ∂ M. We prove that the family of metrics preserves various natural curvature conditions under suitable assumptions on the boundary data. Moreover, under suitable assumptions on the boundary data, we can deform a metric to one with totally geodesic boundary while preserving various natural curvature conditions.

Cited by

• Positive curvature conditions on contractible manifolds

Related

• Prescribing the curvature of Riemannian manifolds with boundary
• Prescribing curvatures on three dimensional Riemannian manifolds with boundaries
• Deformation of the scalar curvature and the mean curvature
• Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary
• Scalar curvature deformations with non-compact boundaries