2013/12/30 by Akito Futaki, Futaki, Akito
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.1312.7607
Minor modifications. Submitted to Shoshichi Kobayashi memorial volume
openalex publication_date 2013/12/30 · arxiv created 2014/04/08 · arxiv updated 2014/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this short note we compare the weighted Laplacians on real and complex (Kähler) metric measure spaces. In the compact case Kähler metric measure spaces are considered on Fano manifolds for the study of Kähler-Einstein metrics while real metric measure spaces are considered with Bakry-Émery Ricci tensor. There are twisted Laplacians which are useful in both cases but look alike each other. We see that if we consider noncompact complete manifolds significant differences appear.