Journal of Differential Geometry

Comparing the Morse index and the first Betti number of minimal hypersurfaces

Lucas Ambrozio, Alessandro Carlotto, and Ben Sharp

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


By extending and generalizing previous work by Ros and Savo, we describe a method to show that in certain positively curved ambient manifolds the Morse index of every closed minimal hypersurface is bounded from below by a linear function of its first Betti number. The technique is flexible enough to prove that such a relation between the index and the topology of minimal hypersurfaces holds, for example, on all compact rank one symmetric spaces, on products of the circle with spheres of arbitrary dimension and on suitably pinched submanifolds of the Euclidean spaces. These results confirm a general conjecture due to Schoen and Marques–Neves for a wide class of ambient spaces.

Article information

J. Differential Geom., Volume 108, Number 3 (2018), 379-410.

Received: 4 February 2016
First available in Project Euclid: 2 March 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Ambrozio, Lucas; Carlotto, Alessandro; Sharp, Ben. Comparing the Morse index and the first Betti number of minimal hypersurfaces. J. Differential Geom. 108 (2018), no. 3, 379--410. doi:10.4310/jdg/1519959621.

Export citation