A Polynomial Solution for the Potato-peeling Problem.
A Proof of a General Isoperimetric Inequality for Surfaces.
A proof of two conjectures related to the Erdős-Debrunner inequality.
A quantitative isoperimetric inequality in n-dimensional space.
A quantitative version of the isoperimetric inequality : the anisotropic case
We state and prove a stability result for the anisotropic version of the isoperimetric inequality. Namely if is a set with small anisotropic isoperimetric deficit, then is “close” to the Wulff shape set.
A refined Brunn-Minkowski inequality for convex sets
A remark about the directed line-elements in the plane
A reverse isoperimetric inequality for convex plane curves.
A separation theorem for finite families
A sequence of inequalities for certain sets of concurrent cevians.
A sharp isoperimetric inequality in the plane
We show that among all the convex bounded domain in having an assigned Fraenkel asymmetry index, there exists only one convex set (up to a similarity) which minimizes the isoperimetric deficit. We also show how to construct this set. The result can be read as a sharp improvement of the isoperimetric inequality for convex planar domain.
A sharpening of a discrete analog of Wirtinger's and isoperimetric inequalities
A sharpening of a discrete case of Wirtinger's inequality is given. It is then used to sharpen the isoperimetric unequality for polygons.
A sharpening of discrete analogues of Wirtinger's inequality
A stability estimate for the Aleksandrow-Fnechel inequality, with an application to mean curvature.
A stability theorem for the area sum of a convex polygon and its polar reciprocal.
A supplement to Eddy's paper.
A weighted geometric inequality and its applications.
About an inequality of Kubota for plane convex figures.
An elementary proof of Blundon's inequality.
An extension of Blaschke's theorem in the plane.