Conformal capacities and conformally invariant functions on Riemannian manifolds |
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Authors: | Jacqueline Ferrand |
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Institution: | (1) University of Paris VI, 14 rue de Bagneux, F-92330 Sceaux, France |
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Abstract: | This paper develops the theory of conformal invariants initiated inJ. Differential Geom
8 (1973), 487–510 for a Riemannian manifoldM with dimensionn2. We construct and study four conformally invariant functions M, M, M, M resp. depending on 4, 3 or 2 points onM, defined as extremal capacities for condensers associated with those points. These functions have similarities with the classical invariants onS
n
,R
n
orH
n
. Their properties, and especially their continuity, are efficient tools for solving some problems of conformal geometry in the large. |
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Keywords: | 30C70 31B15 53A30 51B10 |
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