About

Bennett Chow is a professor in the Department of Mathematics at the University of California, San Diego. He holds a Ph.D. in Mathematics from Princeton University, obtained in 1986. His research areas include Geometric Analysis and Differential Geometry, with specific interests in Geometric Flows, both smooth and discrete. His work focuses on understanding the geometric structures and their evolution, contributing to the broader field of geometric analysis.

Research topics

• Computer Science
• Geometry
• Mathematics
• Physics
• Mathematical analysis
• Pure mathematics
• Mathematical physics

Selected publications

• Richard Streit Hamilton (1943–2024)

  Notices of the American Mathematical Society · 2025-10-01

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• Correction to: Curvature growth of some 4-dimensional gradient Ricci soliton singularity models

  ArXiv.org · 2025-05-03

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  This note corrects an error in the proof of Proposition 13 in arXiv:1903.09181 and simultaneously establishes a more general result. We prove that if $M $ is a compact connected oriented $4$-manifold with connected boundary $\partial M$, and if an unbounded number of disjoint copies of $M$ embed topologically and locally flatly in the interior of a compact $4$-manifold $N,$ then $\operatorname{Tor}H_1(\partial M;\mathbb{Z})$ is a direct double, i.e., $\operatorname{Tor}H_1(\partial M;\mathbb{Z})\cong A \oplus A$, with the linking pairing vanishing identically on the first summand, i.e., the linking pairing is split metabolic. This partially generalizes Hantzsche's theorem stating that the linking pairing for a closed $3$-manifold that embeds in $S^4$ is hyperbolic.

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• Lectures on Differential Geometry

  Graduate studies in mathematics · 2024 · 102 citations

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  • Computer Science
  • Geometry
  • Mathematics
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• Small improvements for a trio of estimates for Ricci solitons

  Proceedings of the American Mathematical Society · 2023-05-24

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  In this note we discuss a trio of estimates for Ricci solitons that only provide glimpses of their asymptotic geometry. Namely, the results hold for some sequence of points tending to infinity in two of the cases, and for a net of points in the remaining case.

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• Aleksandrov reflection for extrinsic geometric flows of Euclidean hypersurfaces

  Advanced Nonlinear Studies · 2023-01-01 · 8 citations

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  Abstract We survey some ideas regarding the application of the Aleksandrov reflection method in partial differential equation to extrinsic geometric flows of Euclidean hypersurfaces. In this survey, we mention some related and important recent developments of others on the convergence of noncontracting flows and construction and classification of ancient flows.

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• Ricci Solitons in Low Dimensions

  Graduate studies in mathematics · 2023-08-09 · 5 citations

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• Lower bounds for the scalar curvatures of Ricci flow singularity models

  Journal für die reine und angewandte Mathematik (Crelles Journal) · 2022-12-14

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  Abstract In a series of papers, Bamler [5, 4, 6] further developed the high-dimensional theory of Hamilton’s Ricci flow to include new monotonicity formulas, a completely general compactness theorem, and a long-sought partial regularity theory analogous to Cheeger–Colding theory. In this paper we give an application of his theory to lower bounds for the scalar curvatures of singularity models for Ricci flow. In the case of 4-dimensional non-Ricci-flat steady soliton singularity models, we obtain as a consequence a quadratic decay lower bound for the scalar curvature.

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• Lower bounds for the scalar curvatures of Ricci flow singularity models

  arXiv (Cornell University) · 2022-08-28

  preprintOpen access

  In a series of papers, Bamler [Bam20a,Bam20b,Bam20c] further developed the high-dimensional theory of Hamilton's Ricci flow to include new monotonicity formulas, a completely general compactness theorem, and a long-sought partial regularity theory analogous to Cheeger--Colding theory. In this paper we give an application of his theory to lower bounds for the scalar curvatures of singularity models for Ricci flow. In the case of $4$-dimensional non-Ricci-flat steady soliton singularity models, we obtain as a consequence a quadratic decay lower bound for the scalar curvature.

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• On four-dimensional steady gradient Ricci solitons that dimension reduce

  Advances in Mathematics · 2022-04-06 · 12 citations

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• Li–Yau Inequalities in Geometric Analysis Dedicated to Professor Peter Li on the occasion of his 70th Birthday

  Journal of Geometric Analysis · 2022-08-24 · 4 citations

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Recent grants

• FRG: Collaborative Research: Heat Equations and Geometric Flows in Riemannian and Kaehler Geometry

  NSF · $282k · 2004–2009

Frequent coauthors

• Christine Guenther

  Pacific University

  67 shared

• Dan Knopf

  65 shared

• Lei Ni

  55 shared

• Sun-Chin Chu

  National Chung Cheng University

  54 shared

• Peng Lü

  Dalian University of Technology

  53 shared

• David Glickenstein

  53 shared

• Tom Ivey

  College of Charleston

  48 shared

• James Isenberg

  University of Oregon

  48 shared