Open AccessA remark on covering of compact Kähler manifolds and applications
Author(s) -
Vũ Văn Hùng,
Hoang Nhat Quy
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i1.6038
Subject(s) - exponent , mathematics , manifold (fluid mechanics) , curvature , base (topology) , upper and lower bounds , cover (algebra) , compact space , algebraic number , kähler manifold , function (biology) , pure mathematics , combinatorics , mathematical analysis , geometry , mechanical engineering , philosophy , linguistics , evolutionary biology , engineering , biology
UDC 517.9Recently, Kolodziej proved that, on a compact Kähler manifold the solutions to the complex Monge – Ampére equation with the right-hand side in are Hölder continuous with the exponent depending on and (see [Math. Ann., 342 , 379-386 (2008)]).Then, by the regularization techniques in[J. Algebraic Geom., 1 , 361-409 (1992)], the authors in [J. Eur. Math. Soc., 16 , 619-647 (2014)] have found the optimal exponent of the solutions.In this paper, we construct a cover of the compact Kähler manifold which only depends on curvature of Then, as an application, base on the arguments in[Math. Ann., 342 , 379-386 (2008)], we show that the solutions are Hölder continuous with the exponent just depending on the function in the right-hand side and upper bound of curvature of