The dissertation is written on the basis of the paper published in Annales Polonici Mathematici, the paper published in Acta Mathematica Vietnamica and the paper published in Results in Mathematics. | VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY INSTITUTE OF MATHEMATICS DO THAI DUONG SOME PROBLEMS IN PLURIPOTENTIAL THEORY DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MATHEMATICS HANOI - 2021 VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY INSTITUTE OF MATHEMATICS DO THAI DUONG SOME PROBLEMS IN PLURIPOTENTIAL THEORY Speciality Mathematical Analysis Speciality code 9460102 62 46 01 02 DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MATHEMATICS Supervisor Prof. . PHAM HOANG HIEP Prof. . DINH TIEN CUONG HANOI - 2021 Confirmation This dissertation was written on the basis of my research works carried out at Institute of Mathematics Vietnam Academy of Science and Technology under the supervision of Prof. . Pham Hoang Hiep and Prof. . Dinh Tien Cuong. All the presented results have never been published by others. January 3 2021 The author Do Thai Duong i Acknowledgments First of all I am deeply grateful to my academic advisors Professor Pham Hoang Hiep and Professor Dinh Tien Cuong for their invaluable help and support. I am sincerely grateful to IMU The International Mathematical Union FIMU Friends of the IMU and TWAS The World Academy of Sciences for supporting my PhD studies through the IMU Breakout Graduate Fellowship. The wonderful research environment of the Institute of Mathematics Vietnam Academy of Science and Technology and the excellence of its staff have helped me to complete this work within the schedule. I would like to thank my colleagues for their efficient help during the years of my PhD studies. Especially I would like to express my special appreciation to Do Hoang Son for his valuable comments and suggestions on my research results. I also would like to thank the participants of the weekly seminar at Department of Mathematical Analysis for many useful conversations. Furthermore I am sincerely grateful to Prof. Le Tuan
