Abstract
We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can “hear” the weights of a weighted projective space.
Similar content being viewed by others
References
Abreu M., Dryden E., Freitas P., Godinho L.: Hearing the weights of weighted projective planes. Ann. Glob. Anal. Geom. 33(4), 373–395 (2007)
Arkhipov, A.: On the pairwise sums problem. SPUR 2008 project report
Duistermaat J.J., Guillemin V.: The spectrum of positive elliptic operators and periodic bicharacteristics. Invent. Math. 29, 37–79 (1975)
Sadovnichi, V.A., Grigoryan, A.A., Konyagin, S.V.: Problems of student mathematical olympiads. Moscow State University, 1987, Problem 19, page 83, Solution 295–296 (1987)
Stanhope, E., Uribe, A.: The spectral function of a Riemannian orbifold (preprint)
Weinstein A.: Symplectic geometry. Bull.AMS 5, 1–13 (1981)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by M. Shubin (Boston).
Rights and permissions
About this article
Cite this article
Guillemin, V., Uribe, A. & Wang, Z. Geodesics on weighted projective spaces. Ann Glob Anal Geom 36, 205–220 (2009). https://doi.org/10.1007/s10455-009-9159-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10455-009-9159-7