https://neckpinch.com/authors/anjali-bhatnagar/New arXiv papers by Anjali Bhatnagar, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2605.25455/arxiv:2605.25455Mon, 25 May 2026 00:00:00 GMTAnjali Bhatnagar, Jiliang Fan — The Fefferman–Szegő metric g_FS^Ω on a C^∞-smooth bounded strongly pseudoconvex domain Ω⊂ℂⁿ is an invariant metric defined via the Fefferman surface measure. For this metric, we first establish the vanishing of its L²-Dolbeault cohomology outside the middle degree: dim H^(p,q)₂(Ω)=0 if p+q≠ n, while dim H^(p,q)₂(Ω)=∞ if p+q=n. We also prove that the metric has C^∞-bounded geometry. Using this analytic property, we obtain several rigidity results. In particular, if the Fefferman–Szegő metric is a gradient Kahler–Ricci soliton, then Ω is biholomorphic to the unit ball Bⁿ. Moreover, if the metric has constant scalar curvature, then it is Einstein, and again Ω is biholomorphic to Bⁿ. We also give a Ramadanov-type criterion in terms of the Fefferman–Szegő invariant function. Finally, in dimension n=2, assuming the existence of a Kahler immersion into a finite-dimensional ball that maps boundary to boundary transversally, we show that the logarithmic term of the Fefferman–Szegő kernel vanishes to infinite order. Consequently, the boundary is locally spherical; if, in addition, Ω is simply connected, then Ω is biholomorphic to B².Ricci solitonsKähler–Ricci solitonsKähler geometryScalar curvatureStability & uniqueness