TY - JOUR
T1 - Rigidity of min-max minimal spheres in three-manifolds
AU - Marques, Fernando C.
AU - Neves, Ndré
PY - 2012/11/1
Y1 - 2012/11/1
N2 - In this paper we consider min-max minimal surfaces in three-manifolds and prove some rigidity results. For instance, we prove that any metric on a three-sphere which has scalar curvature greater than or equal to 6 and is not round must have an embedded minimal sphere of area strictly smaller than 4π and index at most one. If the Ricci curvature is positive we also prove sharp estimates for the width.
AB - In this paper we consider min-max minimal surfaces in three-manifolds and prove some rigidity results. For instance, we prove that any metric on a three-sphere which has scalar curvature greater than or equal to 6 and is not round must have an embedded minimal sphere of area strictly smaller than 4π and index at most one. If the Ricci curvature is positive we also prove sharp estimates for the width.
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U2 - 10.1215/00127094-1813410
DO - 10.1215/00127094-1813410
M3 - Article
AN - SCOPUS:84871289657
VL - 161
SP - 2725
EP - 2752
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
SN - 0012-7094
IS - 14
ER -