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14 papers · 1 filter
New Examples of Obstructions to Non-Negative Sectional Curvatures in Cohomogeneity One Manifolds
Chenxu He
K. Grove, L. Verdiani, B. Wilking and W. Ziller gave the first examples of cohomogeneity one manifolds which do not carry invariant metrics with non-negative sectional curvatures.…
The harmonic mean curvature flow of nonconvex surfaces in
Panagiota Daskalopoulos, Natasa Sesum
We consider a compact, star-shaped, mean convex hypersurface . We prove that in some cases the flow exists until it shrinks to a point in a spherical manne…
Lifting Group Actions and Nonnegative Curvature
Karsten Grove, Wolfgang Ziller
We show that all vector bundles over CP^2 which are not spin admit a complete metric with nonnegative sectional curvature. In the proof we construct a nonnegatively curved metric o…
Rigidity of gradient Ricci Solitons
Peter Petersen, William Wylie
We define a gradient Ricci soliton to be rigid if it is a flat bundle where is Einstein. It is known that not all gradient solitons are rigid. Here…
On gradient Ricci solitons with Symmetry
Peter Petersen, William Wylie
We study gradient Ricci solitons with maximal symmetry. First we show that there are no non-trivial homogeneous gradient Ricci solitons. Thus the most symmetry one can expect is an…
Blocking: New examples and properties of products
Pilar Herreros
We say that a pair of points x and y is secure if there exist a finite set of blocking points such that any geodesic between x and y passes through one of the blocking points. The…