Kazdan inequality

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Let be a real -dimensional scalar inner product space (cf. also Inner product; Pre-Hilbert space), let be the space of linear operators of , and let be a given family of symmetric linear operators depending continuously on . For , denote by the solution of the initial value problem

Suppose that is invertible for all . Then for every positive -function on satisfying on , one has

with equality if and only if for all .


[a1] J.L. Kazdan, "An inequality arising in geometry" A.L. Besse (ed.) , Manifolds all of whose Geodesics are Closed , Springer (1978) pp. 243–246; Appendix E
[a2] I. Chavel, "Riemannian geometry: A modern introduction" , Cambridge Univ. Press (1995)
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Kazdan inequality. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by H. Kaul (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article