Publication

Stability of stationary wave maps from a curved background to a sphere

Sohrab Mirshams Shahshahani
2016
Journal paper
Abstract

We study time and space equivariant wave maps from M×RS2M \times \mathbb{R} \rightarrow S^2, where MM is dieomorphic to a two dimensional sphere and admits an action of SO(2)SO(2) by isometries. We assume that metric on MM can be written as dr2+f2(r)dθ2dr^2+f^2(r)d\theta^2 away from the two xed points of the action, where the curvature is positive, and prove that stationary (time equivariant) rotationally symmetric (of any rotation number) smooth wave maps exist and are stable in the energy topology. The main new ingredient in the construction, compared with the case where MM is isometric to the standard sphere (considered by Shatah and Tahvildar-Zadeh [34]), is the the use of triangle comparison theorems to obtain pointwise bounds on the fundamental solution on a curved background.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.