#### Vol. 299, No. 2, 2019

 Recent Issues Vol. 300: 1  2 Vol. 299: 1  2 Vol. 298: 1  2 Vol. 297: 1  2 Vol. 296: 1  2 Vol. 295: 1  2 Vol. 294: 1  2 Vol. 293: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Special Issues Submission Guidelines Submission Form Contacts Author Index To Appear ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Other MSP Journals
Rigidity theorems of hypersurfaces with free boundary in a wedge in a space form

### Juncheol Pyo

Vol. 299 (2019), No. 2, 489–510
DOI: 10.2140/pjm.2019.299.489
##### Abstract

This paper presents some rigidity results about compact hypersurfaces with free boundary in a wedge in a space form. First, we prove that every compact immersed stable constant mean curvature hypersurface with free boundary in a wedge is part of an intrinsic sphere centered at a point of the edge of the wedge. Second, we show that the same rigidity result holds for a compact embedded constant higher-order mean curvature hypersurface with free boundary in a wedge. Finally, we extend this result to a compact immersed hypersurface with free boundary in a wedge that has the additional property that the ratio of two higher-order mean curvatures is constant.

The same conclusions hold for a compact hypersurface with free boundary that lies in a half-space in a space form.

 Dedicated to Professor Jaigyoung Choe in honor of his 65th birthday.
##### Keywords
intrinsic spheres, surfaces with free boundary, higher-order mean curvature
##### Mathematical Subject Classification 2010
Primary: 53C24, 49Q10