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Mathematics > Differential Geometry

Title: Expanding Ricci solitons coming out of weakly PIC1 metric cones

Abstract: Motivated by recent work of Deruelle-Schulze-Simon, we study complete weakly PIC1 Ricci flows with Euclidean volume growth coming out of metric cones. We show that such a Ricci flow must be an expanding gradient Ricci soliton, and as a consequence, any metric cone at infinity of a complete weakly PIC1 K\"ahler manifold with Euclidean volume growth is biholomorphic to complex Euclidean space in a canonical way.
Comments: 21 pages, minor changes, all comments are welcome
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:2404.12755 [math.DG]
  (or arXiv:2404.12755v2 [math.DG] for this version)

Submission history

From: Pak-Yeung Chan [view email]
[v1] Fri, 19 Apr 2024 10:00:50 GMT (19kb)
[v2] Wed, 1 May 2024 10:38:58 GMT (20kb)

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