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We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if ∆(L) is the order complex of a rank (r +1) geometric lattice L, then the for all i ≤ r...
In this note we prove a new \epsilon-regularity theorem for the Ricci flow. Let (M^n,g(t)) with t\in [-T,0] be a Ricci flow and H_{x} the conjugate heat kernel centered at a point (x,0) in the final t...
Abstract: We prove local Poincar\'e inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we consider is...
Abstract: We prove some Caccioppoli's inequalities for the traceless part of the second fundamental form of a complete, non compact, finite index, constant mean curvature hypersurface of a Riemannian ...
Abstract: In a previous article the author extended the Witten deformation to singular spaces with cone-like singularities and to a class of Morse functions called admissible Morse functions. The meth...
Abstract: In this paper we prove a mass-capacity inequality and a volumetric Penrose inequality for conformally flat manifolds, in arbitrary dimensions. As a by-product of the proofs, capacity and Ale...
We give the generalized triangle inequalities which determine the possible -valued side lengths of n-gons in thick Euclidean buildings of rank 2.
We present in this work a new and shorter proof of the generalized -Newton inequalities for elementary symmetric functions defined on a self-conjugate set which lies essentially in the open right half...
Mixed arithmetic and geometric means, with and without weights, are both considered. Related to mixed arithmetic and geometric means, the following three types of inequalities and their generalization...
Let denote the polar derivative of a polynomial of degree with respect to real or complex number . If does not vanish in EIGHT="32" ALIGN="MIDDLE" BORDER="0" src="images/144_07...
By using subtraction-free expressions, we are able to provide a new proof of the Turán inequalities for the Taylor coefficients of a real entire function when the zeros belong to a specified sector. ...
On surfaces we give conditions under which the solution of a restricted local isoperimetric problem for sectors with small solid angle is the circular sector and we characterize these surfaces. Also w...

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