arXiv:1409.2072 [math.DG]AbstractReferencesReviewsResources
The Mabuchi Geometry of Finite Energy Classes
Published 2014-09-07Version 1
We introduce different Finsler metrics on the space of smooth K\"ahler potentials that will induce a natural geometry on various finite energy classes $\mathcal E_{\tilde \chi}(X,\omega)$. Motivated by questions raised by R. Berman, V. Guedj and Y. Rubinstein, we characterize the underlying topology of these spaces in terms of convergence in energy and give applications of our results to existence of K\"ahler-Einstein metrics on Fano manifolds.
Comments: comments welcome
Related articles: Most relevant | Search more
arXiv:1810.04661 [math.DG] (Published 2018-10-10)
Uniform convexity in $L^p$ Mabuchi geometry, the space of rays, and geodesic stability
arXiv:2212.04110 [math.DG] (Published 2022-12-08)
Hodge Laplacian and geometry of Kuranishi family of Fano manifolds
arXiv:1209.0857 [math.DG] (Published 2012-09-05)
On a new class of Finsler metrics