Abstract:

11D supergravity theory was first constructed by Cremmer, Julia and Scherk, and since then, many special solutions have been found. In the first part of the talk, we describe a geometric construction of solutions to 11D supergravity, which generalizes the famous Duff-Stelle multi-membrane solution. For the second part, we propose a parabolic flow to find more general solutions to 11D supergravity. As a first step, we establish the Shi-type estimate of the flow.