Strong holomorphic Morse inequalities on non-compact complex manifolds with optimal fundamental estimate

TL;DR

This paper proves strong holomorphic Morse inequalities on non-compact complex manifolds by establishing optimal fundamental estimates, extending the inequalities' applicability in complex geometry.

Contribution

It introduces the concept of optimal fundamental estimates and demonstrates their role in validating strong holomorphic Morse inequalities on non-compact manifolds.

Findings

Optimal fundamental estimates are satisfied in various settings.

Strong holomorphic Morse inequalities hold under these estimates.

The results extend Morse inequalities to broader non-compact contexts.

Abstract

In this paper, we establish strong holomorphic Morse inequalities on non-compact manifolds under the condition of optimal fundamental estimates. We show that optimal fundamental estimates are satisfied and then strong holomorphic Morse inequalities hold true in various settings.