@article{Chen2023, 
author = {Zhengmao Chen},
title = {A priori bounds and existence of smooth solutions to Minkowski problems for log-concave measures in warped product space forms},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {6},
pages = {13134-13153},
keywords = {log-concave measure, Minkowski problem, Monge-Ampère equation, the continuous method, warped product space forms},
url = {https://www.sciopen.com/article/10.3934/math.2023663},
doi = {10.3934/math.2023663},
abstract = {In the present paper, we prove the a priori bounds and existence of smooth solutions to a Minkowski type problem for the log-concave measure        e          −      f      (              |            x                        |                2            )        d  x in warped product space forms with zero sectional curvature. Our proof is based on the method of continuity. The crucial factor of the analysis is the a priori bounds of an auxiliary Monge-Ampère equation on              S        n  . The main result of the present paper extends the Minkowski type problem of log-concave measures to the space forms and it may be an attempt to get some new analysis for the log-concave measures.}
}