2014/12/29 by Purvi Gupta, Gupta, Purvi
Mathematics · #32T15 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Metric Geometry (math.MG) #math.CV #math.MG #msc:32T15
paper · pdf · doi:10.48550/arxiv.1412.8253
29 pages, 3 figures; the introduction has been revised substantially; some typos have been fixed; concluding remarks have been dropped; to appear in J. Geom. Anal
openalex publication_date 2014/12/29 · arxiv created 2016/04/30 · arxiv updated 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In convex geometry, the Blaschke surface area measure on the boundary of a convex domain can be interpreted in terms of the complexity of approximating polyhedra. In response to a question raised by D. Barrett, this approach is formulated in the holomorphic setting to establish an alternate interpretation of Fefferman's hypersurface measure on boundaries of strictly pseudoconvex domains in ℂ2. In particular, it is shown that Fefferman's measure can be recovered from the Bergman kernel of the domain. A connection with the geometry of the Heisenberg group, emerging from these results, is also discussed.