Invariant Stein domains in Stein symmetric spaces and a non-linear complex convexity theorem

TL;DR

This paper establishes a complex analogue of Kostant's convexity theorem and applies it to construct G-invariant Grauert tubes in non-compact Riemannian symmetric spaces, advancing the understanding of complex convexity in geometric analysis.

Contribution

It introduces a complex version of Kostant's non-linear convexity theorem and demonstrates its application to G-invariant Grauert tubes in symmetric spaces.

Findings

Proved a complex convexity theorem extending Kostant's result.

Constructed G-invariant Grauert tubes in non-compact symmetric spaces.

Enhanced understanding of complex convexity in geometric analysis.

Abstract

We prove a complex version of Kostant's non-linear convexity theorem. Applications to the construction of G-invariant Grauert tubes of non-compact Riemannian symmetric G/K spaces are given.