Uniform Diameter and Non-collapsing Estimates for Kähler Metrics

Key Points

• The research aims to establish uniform diameter and non-collapsing volume estimates for Kähler metrics.
• Proved uniform diameter estimates for Kähler metrics
• Generalized findings from prior work by Guo-Phong-Song-Sturm
• Addressed similar questions in singular settings
• Demonstrated uniform estimates across a large family of Kähler metrics
• Showed local non-collapsing of volumes in various scenarios