7 papers
Minimal Surfaces with Stratified Branching Sets
Federico Franceschini, Rafe Mazzeo, Paul Minter
Inspired by the Taubes-Wu construction of two-valued harmonic functions by the use of symmetry, we construct minimal surfaces with stratified branching sets as…
ALG gravitational instantons and Hitchin moduli spaces, I: Torelli parameters
Laura Fredrickson, Rafe Mazzeo, Jan Swoboda +1
This is the first of two papers which together prove that the -parameter family of parabolic -Hitchin moduli spaces on the four-punctured sphere are all ALG gravitationa…
An index theorem for Z/2-harmonic spinors branching along a graph
Andriy Haydys, Rafe Mazzeo, Ryosuke Takahashi
We prove an index formula for the Dirac operator acting on two-valued spinors on a -manifold which branch along a smoothly embedded graph , and with respect to…
Solving the Scattering Problem for Open Wave-Guide Networks, III: Radiation Conditions and Uniqueness
Charles L. Epstein, Rafe Mazzeo
This paper continues the analysis of the scattering problem for a network of open wave-guides started in [arXiv:2302.04353, arXiv:2310.05816]. In this part we present explicit, phy…
Tian--Yau metrics: Fredholm theory, Hodge cohomology and moduli spaces
Rafe Mazzeo, Xuwen Zhu
We study the natural geometric elliptic operators on a class of complete Riemannian manifolds which include the 4-dimensional ALH* gravitational instantons and their higher dimensi…
Linear and nonlinear stability for the Bach flow, I
Eric Bahuaud, Christine Guenther, James Isenberg +1
In this paper we prove the linear stability of a gauge-modified version of the Bach flow on any complete manifold (M, h) of constant curvature. This involves some intricate calcula…