Suppose is a compact Kähler manifold. We introduce and explore the metric geometry of the -Calabi Finsler structure on the space of Kähler metrics . After noticing that the -Calabi and -Mabuchi path length topologies on do not typically dominate each other, we focus on the finite entropy space , contained in the intersection of the -Calabi and -Mabuchi completions of and find that after a natural strengthening, the -Calabi and -Mabuchi topologies coincide on . As applications to our results, we give new convergence results for the Kähler–Ricci flow and the weak Calabi flow.
@article{AIHPC_2017__34_5_1131_0, author = {Darvas, Tam\'as}, title = {Comparison of the {Calabi} and {Mabuchi} geometries and applications to geometric flows}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1131--1140}, publisher = {Elsevier}, volume = {34}, number = {5}, year = {2017}, doi = {10.1016/j.anihpc.2016.09.002}, mrnumber = {3742517}, zbl = {1380.58008}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2016.09.002/} }
TY - JOUR AU - Darvas, Tamás TI - Comparison of the Calabi and Mabuchi geometries and applications to geometric flows JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 1131 EP - 1140 VL - 34 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2016.09.002/ DO - 10.1016/j.anihpc.2016.09.002 LA - en ID - AIHPC_2017__34_5_1131_0 ER -
%0 Journal Article %A Darvas, Tamás %T Comparison of the Calabi and Mabuchi geometries and applications to geometric flows %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 1131-1140 %V 34 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2016.09.002/ %R 10.1016/j.anihpc.2016.09.002 %G en %F AIHPC_2017__34_5_1131_0
Darvas, Tamás. Comparison of the Calabi and Mabuchi geometries and applications to geometric flows. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1131-1140. doi : 10.1016/j.anihpc.2016.09.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2016.09.002/
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