Tight maps and holomorphicity, exceptional spaces

TL;DR

This paper proves that tight nonholomorphic maps from irreducible domains into exceptional codomains do not exist, except for known cases involving the Poincaré disc, extending previous results for classical codomains.

Contribution

It establishes the nonexistence of tight nonholomorphic maps into exceptional spaces, broadening the understanding of holomorphicity in geometric mappings.

Findings

No tight nonholomorphic maps into exceptional codomains

Exceptionally, the Poincaré disc admits such maps

Extends previous classical domain results to exceptional spaces

Abstract

We show that there are no tight nonholomorphic maps from irreducible domains into exceptional codomains, the only exception being the already known tight nonholomorphic maps from the Poincare disc. This follows up on previous work by the first author where this was shown for classical codomains.