127 citations · 305 across the 22 of their papers we have counts for
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On the classification of gradient Ricci solitons
Peter Petersen, William Wylie
We show that the only complete shrinking gradient Ricci solitons with vanishing Weyl tensor are quotients of the standard ones. This gives a new proof of the Hamilton-Ivey-Perel'ma…
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…
Comparison Geometry for the Bakry-Emery Ricci Tensor
Guofang Wei, Will Wylie
For Riemannian manifolds with a measure we prove mean curvature and volume comparison results when the -Bakry-Emery Ricci tensor is bounded from belo…
Complete Shrinking Ricci Solitons have Finite Fundamental Group
William Wylie
We show that if a complete Riemannian manifold supports a vector field such that the Ricci tensor plus the Lie derivative of the metric with respect to the vector field has a posit…