TY - JOUR
T1 - The limit spaces of two-dimensional manifolds with uniformly bounded integral curvature
AU - Shioya, Takashi
PY - 1999
Y1 - 1999
N2 - ABSTRACT. We study the class of closed 2-dimensional Riemannian manifolds with uniformly bounded diameter and total absolute curvature. Our first theorem states that this class of manifolds is precompact with respect to the Gromov-Hausdorff distance. Our goal in this paper is to completely characterize the topological structure of all the limit spaces of the class of manifolds, which are, in general, not topological manifolds and even may not be locally 2-connected. We also study the limit of 2-manifolds with Lp-curvature bound forp> 1.
AB - ABSTRACT. We study the class of closed 2-dimensional Riemannian manifolds with uniformly bounded diameter and total absolute curvature. Our first theorem states that this class of manifolds is precompact with respect to the Gromov-Hausdorff distance. Our goal in this paper is to completely characterize the topological structure of all the limit spaces of the class of manifolds, which are, in general, not topological manifolds and even may not be locally 2-connected. We also study the limit of 2-manifolds with Lp-curvature bound forp> 1.
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U2 - 10.1090/s0002-9947-99-02103-0
DO - 10.1090/s0002-9947-99-02103-0
M3 - Article
AN - SCOPUS:22644448306
SN - 0002-9947
VL - 351
SP - 1765
EP - 1801
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 5
ER -