Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 4

Special Issue in honor of Victor Guillemin

Guest Editors: Yael Karshon, Richard Melrose, Gunther Uhlmann, and Alejandro Uribe

Symplectic geometric flows

Pages: 1853 – 1871

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n4.a6

Authors

Teng Fei (Department of Mathematics & Computer Science, Rutgers University, Newark, New Jersey, U.S.A.)

Duong H. Phong (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Abstract

Several geometric flows on symplectic manifolds are introduced which are potentially of interest in symplectic geometry and topology. They are motivated by the Type IIA flow and T‑duality between flows in symplectic geometry and flows in complex geometry. Examples include the Hitchin gradient flow on symplectic manifolds, and a new flow which is called the dual Ricci flow.

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The authors dedicate this paper to the beloved Professor Victor Guillemin. Some ideas behind this paper date back to many conversations the first-named author had with Victor when he was a graduate student at MIT.

The work of Teng Fe was supported in part by Simons Collaboration Grant 853806. The work of Duong H. Phong was supported in part by NSF grant DMS-1855947.

Received 27 November 2021

Accepted 30 May 2022

Published 20 November 2023