caa a22 4500 469068760 CHVBK 20180323132915.0 cr unu---uuuuu 170328e19920601xx s 000 0 eng 10.1007/BF02808163 doi (NATIONALLICENCE)springer-10.1007/BF02808163 Reznikov Alexander Department of Mathematics Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel aut Affine symplectic geometry I: Applications to geometric inequalities [Elektronische Daten] [Alexander Reznikov] We use the integral geometric formulas in the symplectic space of geodesics of a Riemannian manifold to derive various inequalities of isoperimetric type. We give a sharp lower bound for the area of the minimal bubble spanning a spherical curve in ℝ3. We also present an "inverse Croke inequality” relating the area of the boundary of a complex domain in a Riemannian manifold to the injectivity radius and the volume of the domain. We prove a sharp lower bound for the ground state of the harmonic oscillator operator inL 2(M), whereM is a Hadamard manifold. Hebrew University, 1992 Israel Journal of Mathematics Springer-Verlag 80/1-2(1992-06-01), 207-224 0021-2172 80:1-2<207 1992 80 11856 https://doi.org/10.1007/BF02808163 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02808163 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Reznikov Alexander Department of Mathematics Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 80/1-2(1992-06-01), 207-224 0021-2172 80:1-2<207 1992 80 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer