Many shapes resulting from important geometric operations in industrial applications such as Minkowski sums or volume swept by a moving object can be seen as the projection of higher dimensional objects. When such a higher dimensional object is a smooth manifold, the boundary of the projected shape can be computed from the critical points of the projection. In this paper, using the notion of po...

– Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity showed by L. Gross, we prove that logarithmic Sobolev inequalities are related similarly to hypercontractivity of solutions of Hamilton–Jacobi equations. By the infimum-convolution description of the Hamilton–Jacobi solutions, this approach provides a clear view of the connection between logarithmic Sobo...

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit “hidden symmetry” from conformal KillingYano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codimensiontwo submanifold with constant normalized null expansion (null mean curva...

Abstract We prove the validity of p -Brunn–Minkowski inequality for intrinsic volume $$V_k$$ V k , $$k=2,\dots n-1$$ = 2 , ⋯ n - 1 </mml:mro...

We consider a different L-Minkowski combination of compact sets in R than the one introduced by Firey and we prove an L-BrunnMinkowski inequality, p ∈ [0, 1], for a general class of measures called convex measures that includes log-concave measures, under unconditional assumptions. As a consequence, we derive concavity properties of the function t 7→ μ(t 1 pA), p ∈ (0, 1], for unconditional con...

In this article we study stability and compactness w.r.t. measured Gromov-Hausdorff convergence of smooth metric measure spaces with integral Ricci curvature bounds. More precisely, prove that a sequence n -dimensional Riemannian manifolds subconverges to space satisfies the curvature-dimension condition C D ( K , ) in sense Lott-Sturm-Villani provided L p -norm for > 2 part lies below converge...