Add to ORKGWe classify the volume preserving stable hypersurfaces in the real projective space $\mathbb{RP}^n$. As a consequence, the solutions of the isoperimetric problem are tubular neighborhoods of projective subspaces $\mathbb{RP}^k\subset \mathbb{RP}^n$ (starting with points). This confirms a conjecture of Burago and Zalgaller from 1988 and extends to higher dimensions previous result of M. Ritor\'{e} and A. Ros on $\mathbb{RP}^3$. We also derive an Willmore type inequality for antipodal invariant hypersurfaces in $\mathbb{S}^n$.Comment: 19 pages, 1 figur
International audienceConsider an open domain D on the plane, whose isoperimetric deficit is smaller...
We give a notion of stability for constant r-mean curvature hypersurfaces in a general Riemannian ma...
The Euclidean mixed isoperimetric-isodiametric inequality states that the round ball maximizes the v...
We solve the isoperimetric problem in the lens spaces with large fundamental group. Namely, we prove...
We prove that geodesic balls centered at some base point are isoperimetric in the real hyperbolic sp...
We prove a sharp isoperimetric inequality for Finsler manifolds having non-negative Ricci curvature ...
We shall discuss the question of stability of the solution of the classical isoperi-metric problem i...
Abstract. We prove that the area of a hypersurface Σ which traps a given volume outside a convex dom...
We prove that the isoperimetric inequalities in the Euclidean and hyperbolic plane hold for all Eucl...
AbstractGiven a compact Riemannian manifold M without boundary, we show that large isoperimetric reg...
For a domain U on a certain k-dimensional minimal submanifold of S " or H", we introduce ...
In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric...
The Euclidean mixed isoperimetric-isodiametric inequality states that the round ball maximizes the v...
International audienceConsider an open domain D on the plane, whose isoperimetric deficit is smaller...
We prove that if (X, d,m) is a metric measure space with m(X) = 1 having (in a synthetic sense) Ric...
International audienceConsider an open domain D on the plane, whose isoperimetric deficit is smaller...
We give a notion of stability for constant r-mean curvature hypersurfaces in a general Riemannian ma...
The Euclidean mixed isoperimetric-isodiametric inequality states that the round ball maximizes the v...
We solve the isoperimetric problem in the lens spaces with large fundamental group. Namely, we prove...
We prove that geodesic balls centered at some base point are isoperimetric in the real hyperbolic sp...
We prove a sharp isoperimetric inequality for Finsler manifolds having non-negative Ricci curvature ...
We shall discuss the question of stability of the solution of the classical isoperi-metric problem i...
Abstract. We prove that the area of a hypersurface Σ which traps a given volume outside a convex dom...
We prove that the isoperimetric inequalities in the Euclidean and hyperbolic plane hold for all Eucl...
AbstractGiven a compact Riemannian manifold M without boundary, we show that large isoperimetric reg...
For a domain U on a certain k-dimensional minimal submanifold of S " or H", we introduce ...
In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric...
The Euclidean mixed isoperimetric-isodiametric inequality states that the round ball maximizes the v...
International audienceConsider an open domain D on the plane, whose isoperimetric deficit is smaller...
We prove that if (X, d,m) is a metric measure space with m(X) = 1 having (in a synthetic sense) Ric...
International audienceConsider an open domain D on the plane, whose isoperimetric deficit is smaller...
We give a notion of stability for constant r-mean curvature hypersurfaces in a general Riemannian ma...
The Euclidean mixed isoperimetric-isodiametric inequality states that the round ball maximizes the v...