6. Analysis Seminar:
Speaker: Utsav Dewan (ISI Kolkata)
Title: Boundary exceptional sets for radial limits of positive superharmonic functions on Harmonic manifolds
Time, Day and Date: 4:00 p.m., Thursday,  September 5
Venue: Ramanujan Hall, Department of Mathematics
Abstract: By classical Fatou (resp. Littlewood) type theorems in various setups, it is well-known that positive harmonic (resp. superharmonic) functions have non-tangential (resp. radial) limits at almost every point on the boundary. In this talk, in the setting of non-positively curved Harmonic manifolds of purely exponential volume growth, we will see some size estimates of the exceptional sets of points on the boundary at infinity, where a suitable function blows up faster than a prescribed growth rate, along radial geodesic rays, in terms of its Hausdorff dimension or Hausdorff outer measure.