Dynamics of Partial Differential Equations

Volume 14 (2017)

Number 4

Inverse spectral theory and the Minkowski problem for the surface of revolution

Pages: 321 – 341

DOI: http://dx.doi.org/10.4310/DPDE.2017.v14.n4.a1


Hiroshi Isozaki (Institute of Mathematics, University of Tsukuba, Japan)

Evgeny L. Korotyaev (Saint-Petersburg State University, St. Petersburg, Russia)


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

35-xx, 51-xx

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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.

Received 19 May 2016

Published 14 December 2017