The eternal solution to the cross curvature flow exists in 3-manifolds of negative sectional curvature

Authors

WEIHUNG LIAO

DOI

10.3906/mat-1812-90

Abstract

Given a closed 3-manifold $M^3$ endowed with a radial symmetric metric of negative sectional curvature, we define the cross curvature flow on $M^3$; using the maximum principle theorem, we demonstrated that the solution to the cross curvature flow exists for all time and converges pointwise to a hyperbolic metric.

Keywords

Cross curvature flow, geometric evolution equation, negative sectional curvature

First Page

2444

Last Page

2450

Recommended Citation

LIAO, WEIHUNG (2019) "The eternal solution to the cross curvature flow exists in 3-manifolds of negative sectional curvature," Turkish Journal of Mathematics: Vol. 43: No. 5, Article 31. https://doi.org/10.3906/mat-1812-90
Available at: https://journals.tubitak.gov.tr/math/vol43/iss5/31