TY - JOUR
AU - V. V. Hung
AU - H. N. Quy
PY - 2021/01/22
Y2 - 2022/08/13
TI - A remark on covering of compact Kähler manifolds and applications
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 73
IS - 1
SE - Research articles
DO - 10.37863/umzh.v73i1.6038
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/6038
AB - UDC 517.9Recently, Kolodziej proved that, on a compact Kähler manifold $M,$ the solutions to the complex Monge – Ampére equation with the right-hand side in $L^p,$ $p>1,$ are Hölder continuous with the exponent depending on $M$ and $\|f\|_p$ (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 $M$ which only depends on curvature of $M.$ 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 $f$ in the right-hand side and upper bound of curvature of $M.$
ER -