Abstract
Gaussian dual curvature measure is introduced and Gaussian dual Minkowski problem is studied. This problem amounts to solving a class of Monge-Ampère type equations on the unit sphere. Existence and uniqueness of solutions to the relevant Monge-Ampère type equations are obtained in the smooth category when q≤0, respectively. For q<0, a complete solution to existence part of the Gaussian dual Minkowski problem is presented. For the case of q=0, a weak solution to the Monge-Ampère type equation related to this problem is provided when given measure has the density f which is sandwiched between two positive constants belonging to the interval 0 to 1.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
