Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

4 Issues per year


IMPACT FACTOR 2017: 0.734

CiteScore 2017: 0.70

SCImago Journal Rank (SJR) 2017: 0.695
Source Normalized Impact per Paper (SNIP) 2017: 0.891

Mathematical Citation Quotient (MCQ) 2017: 0.62

Online
ISSN
1615-7168
See all formats and pricing
More options …
Volume 16, Issue 2

Issues

Stable hypersurfaces in spheres with constant scalar curvature

Peng Zhu
  • Corresponding author
  • School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, 213001, Jiangsu, People’s Republic of China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Yadong Jin
  • School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, 213001, Jiangsu, People’s Republic of China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-04-16 | DOI: https://doi.org/10.1515/advgeom-2016-0004

Abstract

We study complete noncompact 1-minimal stable hypersurfaces M in Sn+1. We obtain that there is no stable complete noncompact 1-minimal hypersurface in S4 with nonzero Gauss-Kronecker curvature and _nite total curvature. We show that there is no stable complete noncompact 1-minimal hypersurface in S4 with polynomial volume growth, nonzero Gauss-Kronecker curvature and supM H2 < 5/2. At last, we discuss stable complete noncompact hypersurfaces M with constant scalar curvature R > 1 in Sn+1 and show another nonexistence result. These results are generalised versions of results of Alencar, Santos, Zhou and Silva Neto on stable hypersurfaces in Rn+1 with constant scalar curvature.

Keywords: Constant scalar curvature; stable 1-minimal hypersurface

About the article

Received: 2014-05-19

Published Online: 2016-04-16

Published in Print: 2016-04-01


Citation Information: Advances in Geometry, Volume 16, Issue 2, Pages 199–204, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2016-0004.

Export Citation

© 2016 by Walter de Gruyter Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in