Basic concepts by V.M.Miklyukov and M.-K.Vuorinen. Let be an n-dimensional connected noncompact Riemannian С 2 -manifold without boundary. For where. - презентация

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2 Basic concepts by V.M.Miklyukov and M.-K.Vuorinen. Let be an n-dimensional connected noncompact Riemannian С 2 -manifold without boundary. For where

3 Isoperimetric profile

4 The constant which characterizes isoperimetric profile

5 Theorem (V.M.Miklyukov and M.-K.Vuorinen, 1999) Let. If has an isoperimetric profile with B

6 S.T. Yau result ( 1975) Let be Riemannian manifold, with Gaussian curvature K and k=const

7 Case when the domain is the strip on the plane

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10 Hardy inequality for the strip

11 Comparison of constants B in some special cases when p=q

12 References 1. Ф.Г. Авхадиев, Неравенства для интегральных характеристик областей, Учебное пособие, Казань, КГУ, 2006 – 142 с. 2. V.M.Miklyukov, M.K.Vuorinen, Hardys inequality for -functions on riemanian manifolds // Proc. Amer. Math. Soc. 127, 9 (1999) F.G. Avkhadiev, K.J. Wirths, Unified Poincare and Hardy inequality sharp constants for convex domains, Z.Angev.Math.Meth. 87, No 8-9, (2007) 4. S.T.Yau, Isoperimetric constants and the first eigenvalue of a compact Riemanian manifold, Ann.Sci. Ecole Norm. Sup. (4) 8 (1975), В.М.Миклюков, Неравенство Харди для функций с обобщенными производными на римановых многообразиях. Trudy IPMM NAN Ukrainy. v c