The marked length spectrum of surfaces without conjugate points. (Le spectre marqué des longueurs des surfaces sans points conjugués.) (French) Zbl 0901.58065

Fathi, Albert

C. R. Acad. Sci., Paris, Sér. I 309, No. 9, 621-624 (1989).

Summary: We show how to adapt the methods of Jean-Pierre Otal to prove the marked length spectrum conjecture in the case where one metric has no conjugate points and the second metric has curvature \(\leq 0\) with the set where the curvature is 0 having empty interior.

MSC:

58J50	Spectral problems; spectral geometry; scattering theory on manifolds
53C20	Global Riemannian geometry, including pinching

Keywords:

marked length spectrum conjecture; no conjugate points