2015 | OriginalPaper | Buchkapitel
The Weighted Laplacians on Real and Complex Metric Measure Spaces
verfasst von : Akito Futaki
Erschienen in: Geometry and Analysis on Manifolds
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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.