Dynamics of Partial Differential Equations
Volume 14 (2017)
Inverse spectral theory and the Minkowski problem for the surface of revolution
Pages: 321 – 341
We solve the inverse spectral problem for rotationally symmetric manifolds, which include a class of surfaces of revolution, by giving an analytic isomorphism from the space of spectral data onto the space of functions describing the radius of rotation. An analogue of the Minkowski problem is also solved.
rotationally symmetric manifolds, inverse problem
2010 Mathematics Subject Classification
Various parts of this paper were written during Evgeny Korotyaev’s stay in the Mathematical Institute of University of Tsukuba, Japan and Mittag-Leffler Institute, Sweden. He is grateful to the institutes for the hospitality. His study was supported by the RSF grant No. 15-11-30007. H. Isozaki is partially supported by Grants-in-Aid for Scientific Research (S) 15H05740, and Grants-in-Aid for Scientific Research (B) 16H03944, Japan Society for the Promotion of Science.
Paper received on 19 May 2016.