Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Minimal immersions of compact bordered Riemann surfaces with free boundary
HTML articles powered by AMS MathViewer

by Jingyi Chen, Ailana Fraser and Chao Pang PDF
Trans. Amer. Math. Soc. 367 (2015), 2487-2507 Request permission

Abstract:

Let $N$ be a complete, homogeneously regular Riemannian manifold of dim$N \geq 3$ and let $M$ be a compact submanifold of $N$. Let $\Sigma$ be a compact orientable surface with boundary. We show that for any continuous $f: \left ( \Sigma , \partial \Sigma \right ) \rightarrow \left ( N, M \right )$ for which the induced homomorphism $f_{*}$ on certain fundamental groups is injective, there exists a branched minimal immersion of $\Sigma$ solving the free boundary problem $\left ( \Sigma , \partial \Sigma \right ) \rightarrow \left ( N, M \right )$, and minimizing area among all maps which induce the same action on the fundamental groups as $f$. Furthermore, under certain nonnegativity assumptions on the curvature of a $3$-manifold $N$ and convexity assumptions on the boundary $M=\partial N$, we derive bounds on the genus, number of boundary components and area of any compact two-sided minimal surface solving the free boundary problem with low index.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 58E12, 53C21, 53C43
  • Retrieve articles in all journals with MSC (2010): 58E12, 53C21, 53C43
Additional Information
  • Jingyi Chen
  • Affiliation: Department of Mathematics, The University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada
  • Email: jychen@math.ubc.ca
  • Ailana Fraser
  • Affiliation: Department of Mathematics, The University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada
  • MR Author ID: 662533
  • Email: afraser@math.ubc.ca
  • Chao Pang
  • Affiliation: Department of Mathematics, The University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada
  • Email: ottokk@math.ubc.ca
  • Received by editor(s): September 5, 2012
  • Published electronically: November 24, 2014
  • Additional Notes: This work was partially supported by NSERC
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 2487-2507
  • MSC (2010): Primary 58E12; Secondary 53C21, 53C43
  • DOI: https://doi.org/10.1090/S0002-9947-2014-05990-4
  • MathSciNet review: 3301871