MINIMAL SURFACES IN FINITE VOLUME NONCOMPACT HYPERBOLIC 3-MANIFOLDS (vol 209, pg 617, 2017)

被引:5
|
作者
Collin, Pascal [1 ]
Hauswirth, Laurent [2 ]
Mazet, Laurent [3 ]
Rosenberg, Harold [4 ]
机构
[1] Univ Paul Sabatier, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse, France
[2] Univ Paris Est, CNRS, UPEM, LAMA,UMR 8050, F-77454 Marne La Vallee, France
[3] Univ Tours, Univ Orldans, CNRS, Inst Denis Poisson,UMR 7013, Parc Grandmont, F-37200 Tours, France
[4] Inst Nacl Matemat Pura & Aplicada IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil
关键词
HYPERSURFACES;
D O I
10.1090/tran/7814
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this note, we explain how a mistake made in [2] can be corrected. Actually, this mistake appears in the proof of [2, Proposition 8] (the second maximum principle) and was brought to our attention by Song [4]. Let us notice that unfortunately, we did not find an alternative proof of this proposition, but we found an alternative proposition. The new proposition does not change the subsequent applications we made of the original proposition. At the end of the note, we explain which modifications should be done where the original Proposition 8 is applied. The difference from the original Proposition 8 is that here we have to assume a control on the index of the minimal surface Sigma.
引用
收藏
页码:7521 / 7524
页数:4
相关论文
共 50 条
  • [1] MINIMAL SURFACES IN FINITE VOLUME NONCOMPACT HYPERBOLIC 3-MANIFOLDS
    Collin, Pascal
    Hauswirth, Laurent
    Mazet, Laurent
    Rosenberg, Harold
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (06) : 4293 - 4309
  • [2] Minimal Surfaces in Hyperbolic 3-Manifolds
    Coskunuzer, Baris
    COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2021, 74 (01) : 114 - 139
  • [3] SURFACES IN NONCOMPACT 3-MANIFOLDS
    TUCKER, TW
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (01): : A229 - A229
  • [4] On the construction of minimal foliations by hyperbolic surfaces on 3-manifolds
    Alcalde Cuesta, Fernando
    Dal'Bo, Francoise
    Martinez, Matilde
    Verjovsky, Alberto
    REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2019, 113 (04) : 4127 - 4144
  • [5] Noncompact Fuchsian and quasi-Fuchsian surfaces in hyperbolic 3-manifolds
    Adams, Colin
    ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2007, 7 : 565 - 582
  • [6] On the construction of minimal foliations by hyperbolic surfaces on 3-manifolds
    Fernando Alcalde Cuesta
    Françoise Dal’Bo
    Matilde Martínez
    Alberto Verjovsky
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019, 113 : 4127 - 4144
  • [7] MINIMAL AREA SURFACES AND FIBERED HYPERBOLIC 3-MANIFOLDS
    Farre, James
    Pallete, Franco Vargas
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 150 (11) : 4931 - 4946
  • [8] CLOSED MINIMAL-SURFACES IN HYPERBOLIC 3-MANIFOLDS
    UHLENBECK, KK
    ANNALS OF MATHEMATICS STUDIES, 1983, (103): : 147 - 168
  • [9] MINIMAL SURFACES IN FINITE VOLUME HYPERBOLIC 3-MANIFOLDS N AND IN M x S1, M A FINITE AREA HYPERBOLIC SURFACE
    Collin, P.
    Hauswirth, L.
    Rosenberg, H.
    AMERICAN JOURNAL OF MATHEMATICS, 2018, 140 (04) : 1075 - 1112
  • [10] Minimal surfaces near short geodesics in hyperbolic 3-manifolds
    Mazet, Laurent
    Rosenberg, Harold
    ADVANCES IN MATHEMATICS, 2020, 372