- Turkish Journal of Mathematics
- Vol: 43 Issue: 5
- The eternal solution to the cross curvature flow exists in 3-manifolds of negative sectional curvatu...
The eternal solution to the cross curvature flow exists in 3-manifolds of negative sectional curvature
Authors : Weihung Liao
Pages : 2444-2450
View : 8 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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