The Exponential Decay of Gluing Maps for $J$-Holomorphic map Moduli Spaces

TL;DR

This paper proves that the derivatives of gluing maps for $J$-holomorphic map moduli spaces decay exponentially as the gluing parameter varies, providing key analytical estimates for these geometric structures.

Contribution

It establishes the exponential decay of derivatives of gluing maps, a novel analytical result crucial for understanding the structure of $J$-holomorphic moduli spaces.

Findings

Exponential decay of the derivative of gluing maps is proven.

Provides analytical estimates essential for moduli space analysis.

Enhances understanding of the geometric structure of $J$-holomorphic maps.

Abstract

We prove the exponential decay of the derivative of the gluing maps with respect to the gluing parameter.