Proceedings of the American Mathematical Society

Author(s): Vladimir M. Miklyukov; Matti K. Vuorinen
Journal: Proc. Amer. Math. Soc. 127 (1999), 2745-2754.
MSC (1991): Primary 53C21
Posted: April 23, 1999
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Abstract: We prove that for every Riemannian manifold $\mathcal{X}$ with the isoperimetric profile of particular type there holds an inequality of Hardy type for functions of the class $W_0^{1,p}( \mathcal{X})$ . We also study manifolds satisfying Hardy's inequality and, in particular, we establish an estimate for the rate of growth of the weighted volume of the noncompact part of such a manifold.

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Vladimir M. Miklyukov
Affiliation: Department of Mathematics, Volgograd State University, 2 Prodolnaya 30, Volgograd 400062, Russia
Address at time of publication: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: miklukov@math.vgu.tsaritsyn.su, miklyuk@math.byu.edu

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