Rigidity of proper holomorphic maps between balls with H\"older boundary regularity

TL;DR

This paper proves a rigidity theorem for proper holomorphic maps between unit balls that extend to boundary maps with H"older continuity exceeding 1/2, highlighting the influence of boundary regularity on map rigidity.

Contribution

It establishes a new rigidity result for proper holomorphic maps with boundary regularity greater than 1/2, expanding understanding of boundary behavior in complex analysis.

Findings

Proper holomorphic maps with H"older boundary extension > 1/2 are rigid.

Boundary regularity influences the rigidity of holomorphic maps.

The result applies to maps with many symmetries between unit balls.

Abstract

In this paper, we prove a rigidity result for proper holomorphic maps between unit balls that have many symmetries and which extend to H\"older continuous maps on the boundary, with H\"older exponent strictly greater than 1/2.