# Mathematical Sciences Research Institute

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# Seminar

MLA - Weekly Seminar (Part 2): Sharp stability estimate for tensor tomography in non-positive curvature October 23, 2019 (03:30 PM PDT - 04:30 PM PDT)
Parent Program: Microlocal Analysis MSRI: Simons Auditorium
Speaker(s) Gabriel Paternain (Center for Mathematical Sciences)
Description No Description
Video
Abstract/Media

I will discuss a stability estimate for the geodesic X-ray transform acting on solenoidal tensor fields on a compact simply connected manifold with strictly convex boundary and non-positive curvature.

The estimate is of the form $L^2\mapsto H^{1/2}_{T}$, where the $H^{1/2}_{T}$-space is defined using the natural parametrization of geodesics as initial boundary points and incoming directions (fan-beam geometry). Only tangential derivatives at the boundary are used. The proof is based on the observation that the Pestov identity with boundary term localizes in frequency. This estimate answers a question raised by Boman and Sharafutdinov.