Normalized Ricci flow on a geodesic ball in hyperbolic space with prescribed boundary mean curvature exists forever and converges to a complete hyperbolic metric.
Friedman,Partial differential eqautions of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, NJ
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Normalized Ricci flow on geodesic balls in hyperbolic space with non-decreasing rotationally symmetric boundary mean curvature exists for all time and converges to a hyperbolic metric.
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A Loewner-Nirenberg phenomena for Ricci flow on compact manifolds with boundary
Normalized Ricci flow on a geodesic ball in hyperbolic space with prescribed boundary mean curvature exists forever and converges to a complete hyperbolic metric.
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A Loewner-Nirenberg phenomena for Ricci flow on compact manifolds with boundary.II
Normalized Ricci flow on geodesic balls in hyperbolic space with non-decreasing rotationally symmetric boundary mean curvature exists for all time and converges to a hyperbolic metric.