Hoelder regularity for the spectrum of translation flows

Boris Solomyak

We consider generic translation flows corresponding to Abelian differentials on flat surfaces of genus g≥2g≥2. These flows are weakly mixing by the Avila-Forni theorem. Recently Forni obtained Hoelder estimates on spectral measures for almost all translation flows, following earlier work by Bufetov and myself in genus two. Combining Forni's idea with our methods, we were able to extend our proof to the case of arbitrary genus g≥2g≥2. The proof uses a quantitative Veech criterion a version of Erd\H{o}s-Kahane argument in vector form.

http://scgp.stonybrook.edu/video_portal/video.php?id=4442

Simons- Program: Renormalization and universality in Conformal Geometry, Dynamics, Random Processes, and Field Theory