Non compact boundaries of complex analytic varieties in Hilbert spaces

TL;DR

This paper investigates the boundary problem for complex varieties with isolated singularities in Hilbert spaces, extending methods from compact cases to non-compact varieties within strongly convex open sets.

Contribution

It extends boundary problem solutions to non-compact complex varieties with isolated singularities in Hilbert spaces using hyperplane cuts and previous compact case results.

Findings

Extended boundary problem solutions to non-compact varieties

Applied hyperplane slicing method in Hilbert spaces

Built on previous compact case results

Abstract

We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H. We deal with the problem by cutting with a family of complex hyperplanes in the fashion of [2] and applying the first named author's result for the compact case [13].