Global existence of small equivariant wave maps on rotationally symmetric manifolds

Abstract

We introduce a class of rotationally invariant manifolds, which we call \emph{admissible}, on which the wave flow satisfies smoothing and Strichartz estimates. We deduce the global existence of equivariant wave maps from admissible manifolds to general targets, for small initial data of critical regularity $H^{\frac{n}{2}}$. The class of admissible manifolds includes in particular asymptotically flat manifolds and perturbations of real hyperbolic spaces ${\mathbb{H}}^n$ for $n\ge 3$.

arXiv comment32 pages

References in corpus (7)

• Global regularity of wave maps II. Small energy in two dimensions
• Renormalization and blow up for charge one equivariant critical wave maps
• Regularity of Wave-Maps in dimension 2+1
• Energy dispersed large data wave maps in 2+1 dimensions
• Nonlinear Schrödinger equation on real hyperbolic spaces
• Global regularity of wave maps I. Small critical Sobolev norm in high dimension
• Global Regularity of Wave Maps from R^{3+1} to H^2

Cited by in corpus (1)

• Global existence of Dirac-wave maps with curvature term on expanding spacetimes