Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 033, 7 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.033
(Mi sigma1570)
 

This article is cited in 6 scientific papers (total in 6 papers)

Nonnegative Scalar Curvature and Area Decreasing Maps

Weiping Zhang

Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, P.R. China
Full-text PDF (335 kB) Citations (6)
References:
Abstract: Let $\big(M,g^{TM}\big)$ be a noncompact complete spin Riemannian manifold of even dimension $n$, with $k^{TM}$ denote the associated scalar curvature. Let $f\colon M\rightarrow S^{n}(1)$ be a smooth area decreasing map, which is locally constant near infinity and of nonzero degree. We show that if $k^{TM}\geq n(n-1)$ on the support of ${\rm d}f$, then $ \inf \big(k^{TM}\big)<0$. This answers a question of Gromov. We use a simple deformation of the Dirac operator to prove the result. The odd dimensional analogue is also presented.
Keywords: scalar curvature, spin manifold, area decreasing map.
Funding agency Grant number
National Natural Science Foundation of China 11931007
This work was partially supported by NNSFC Grant no. 11931007.
Received: December 18, 2019; in final form April 15, 2020; Published online April 22, 2020
Bibliographic databases:
Document Type: Article
MSC: 53C27, 57R20, 58J20
Language: English
Citation: Weiping Zhang, “Nonnegative Scalar Curvature and Area Decreasing Maps”, SIGMA, 16 (2020), 033, 7 pp.
Citation in format AMSBIB
\Bibitem{Zha20}
\by Weiping~Zhang
\paper Nonnegative Scalar Curvature and Area Decreasing Maps
\jour SIGMA
\yr 2020
\vol 16
\papernumber 033
\totalpages 7
\mathnet{http://mi.mathnet.ru/sigma1570}
\crossref{https://doi.org/10.3842/SIGMA.2020.033}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000528033700001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85084843088}
Linking options:
  • https://www.mathnet.ru/eng/sigma1570
  • https://www.mathnet.ru/eng/sigma/v16/p33
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:187
    Full-text PDF :26
    References:21
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024