Area-Minimizing Projective Planes in 3-Manifolds
Publication
, Journal Article
Bray, H; Brendle, S; Eichmair, M; Neves, A
Published in: Communications on Pure and Applied Mathematics
September 1, 2010
Let (M, g) be a compact Riemannian manifold of dimension 3, and let F denote the collection of all embedded surfaces homeomorphic to R{double-struck}P{double-struck}2. We study the infimum of the areas of all surfaces in F . This quantity is related to the systole of .M; g/. It makes sense whenever F is nonempty. In this paper, we give an upper bound for this quantity in terms of the minimum of the scalar curvature of (M, g) Moreover, we show that equality holds if and only if (M, g) is isometric to R{double-struck}P{double-struck}3 up to scaling. The proof uses the formula for the second variation of area and Hamilton's Ricci flow. © 2010 Wiley Periodicals, Inc.
Duke Scholars
Published In
Communications on Pure and Applied Mathematics
DOI
EISSN
0010-3640
ISSN
0010-3640
Publication Date
September 1, 2010
Volume
63
Issue
9
Start / End Page
1237 / 1247
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Bray, H., Brendle, S., Eichmair, M., & Neves, A. (2010). Area-Minimizing Projective Planes in 3-Manifolds. Communications on Pure and Applied Mathematics, 63(9), 1237–1247. https://doi.org/10.1002/cpa.20319
Bray, H., S. Brendle, M. Eichmair, and A. Neves. “Area-Minimizing Projective Planes in 3-Manifolds.” Communications on Pure and Applied Mathematics 63, no. 9 (September 1, 2010): 1237–47. https://doi.org/10.1002/cpa.20319.
Bray H, Brendle S, Eichmair M, Neves A. Area-Minimizing Projective Planes in 3-Manifolds. Communications on Pure and Applied Mathematics. 2010 Sep 1;63(9):1237–47.
Bray, H., et al. “Area-Minimizing Projective Planes in 3-Manifolds.” Communications on Pure and Applied Mathematics, vol. 63, no. 9, Sept. 2010, pp. 1237–47. Scopus, doi:10.1002/cpa.20319.
Bray H, Brendle S, Eichmair M, Neves A. Area-Minimizing Projective Planes in 3-Manifolds. Communications on Pure and Applied Mathematics. 2010 Sep 1;63(9):1237–1247.
Published In
Communications on Pure and Applied Mathematics
DOI
EISSN
0010-3640
ISSN
0010-3640
Publication Date
September 1, 2010
Volume
63
Issue
9
Start / End Page
1237 / 1247
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics