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An Inequality between Energy and Intersection
Author(s) -
Croke C.,
Fathi A.
Publication year - 1990
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/22.5.489
Subject(s) - mathematics , intersection (aeronautics) , class (philosophy) , homotopy , identity (music) , inequality , riemannian manifold , manifold (fluid mechanics) , pure mathematics , mathematical analysis , geography , computer science , artificial intelligence , cartography , mechanical engineering , physics , acoustics , engineering
We prove that the identity map on a closed Riemannian manifold without conjugate points is energyminimizing in its homotopy class. For this we introduce a quantity called intersection and we establish an inequality between energy and intersection.