Rigidity of proper holomorphic maps among generalized balls with Levi-degenerate boundaries

TL;DR

This paper extends rigidity results for proper holomorphic maps to a broader class of generalized balls with possibly Levi-degenerate boundaries, using moduli space analysis.

Contribution

It generalizes previous rigidity theorems to include domains with Levi-degenerate boundaries by analyzing the structure of moduli spaces of projective linear subspaces.

Findings

Rigidity theorems established for proper holomorphic maps among generalized balls with Levi-degenerate boundaries.

Generalization of earlier results from Levi-nondegenerate to Levi-degenerate boundary cases.

Use of moduli space structure to analyze and prove rigidity properties.

Abstract

In this paper we studied a broader type of generalized balls which are domains on the complex projective with possibly Levi-degenerate boundaries. We proved rigidity theorems for proper holomorphic mappings among them by exploring the structure of the moduli spaces of projective linear subspaces, which generalized some earlier results for the ordinary generalized balls with Levi-nondegenerate boundaries.