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Using the weak solution of Inverse mean curvature flow, we prove the sharp Minkowski-type inequality for outward minimizing hypersurfaces in Schwarzschild space.

Soit G un groupe algbrique complexe quasi-simple et G/P une varit de drapeaux partiels. La projection sur G/P des varits de Richardson (de la varit des drapeaux complets) forment une stratification de G/P. Nous montrons que les relations dadhrence des varits de Richardson projetes correspondent celles dun certain sous-ensemble de varits de Schubert sur la varit de drapeaux affine de G. Nous comparons aussi les classes de cohomologie quivariante et de K-thorie de ces deux stratifications. Notre travail gnralise celui de Knutson, Lam et Speyer pour la grassmannienne de type A.

We prove$L$^{$q$}-inequalities for the gradient of the Green potential ($Gf$) in bounded, connected NTA-domains in$R$^{$n$},$n$≥2. These domains may have a highly non-rectifiable boundary and in the plane the set of all bounded simply connected NTA-domains coincides with the set of all quasidiscs. We get a restriction on the exponent$q$for which our inequalities are valid in terms of the validity of a reverse Hölder inequality for the Green function close to the boundary.

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