Vol. 14, No. 5, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 6, 1671–1976
Issue 5, 1333–1669
Issue 4, 985–1332
Issue 3, 667–984
Issue 2, 323–666
Issue 1, 1–322

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Parabolic dimensional reductions of 11-dimensional supergravity

Teng Fei, Bin Guo and Duong H. Phong

Vol. 14 (2021), No. 5, 1333–1361
Abstract

Ansatze are constructed under which the solutions of 11-dimensional supergravity must be stationary points of a parabolic flow on a Riemannian manifold M10p . This parabolic flow turns out to be the Ricci flow coupled to a scalar field, a (3p)-form, and a 4-form. This allows the introduction of techniques from parabolic partial differential equations to the search of solutions to 11-dimensional supergravity. As a first step, Shi-type estimates and criteria for the long-time existence of the flow are established.

Keywords
11-dimensional supergravity, Shi-type estimates
Mathematical Subject Classification 2010
Primary: 53Z05
Milestones
Received: 4 August 2018
Accepted: 27 January 2020
Published: 22 August 2021
Authors
Teng Fei
Department of Mathematics
Columbia University
New York, NY
United States
Bin Guo
Department of Mathematics
Columbia University
New York, NY
United States
Duong H. Phong
Department of Mathematics
Columbia University
New York, NY
United States