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Noncompact shrinking four solitons with nonnegative curvature
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Aaron Naber
Published/Copyright:
August 11, 2010
Abstract
We prove that if (M, g, X) is a noncompact four dimensional shrinking soliton with bounded nonnegative curvature operator, then (M, g) is isometric to 
or a finite quotient of 
or S3 × ℝ. In the process we also show that a complete shrinking soliton (M, g, X) with bounded curvature is gradient and κ-noncollapsed and the dilation of a Type I singularity is a shrinking soliton. Further in dimension three we show shrinking solitons with bounded curvature can be classified under only the assumption of Rc ≧ 0. The proofs rely on the technical construction of a singular reduced length function, a function which behaves as the reduced length function but can be extended to singular times.
Received: 2008-03-14
Revised: 2009-04-14
Published Online: 2010-08-11
Published in Print: 2010-August
© Walter de Gruyter Berlin · New York 2010
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- Formules de caractères pour l'induction automorphe
- Duality theorems for slice hyperholomorphic functions
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- Noncompact shrinking four solitons with nonnegative curvature
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Articles in the same Issue
- La filtration de Harder-Narasimhan des schémas en groupes finis et plats
- Formules de caractères pour l'induction automorphe
- Duality theorems for slice hyperholomorphic functions
- Counting points of homogeneous varieties over finite fields
- Noncompact shrinking four solitons with nonnegative curvature
- Free analysis questions II: The Grassmannian completion and the series expansions at the origin
