6 citations · 11 across the 8 of their papers we have counts for
11 papers
On Critical nets in
Antoine Gournay, Yashar Memarian
Critical nets in (sometimes called geodesic nets) are embedded graph with the property that their embedding is a critical point of the total (edge) length functional…
The Isoperimetric Inequality for Compact Rank One Symmetric Spaces and Beyond
Yashar Memarian
Klartag's needle decomposition technique enables one to obtain strong isoperimetric inequalities on Riemannian manifolds other than the classical known examples. As a result, in th…
Spherical Localisation in Convex and Metric Geometry
Yashar Memarian
Spherical localisation is a technique whose history goes back to M.Gromov and V.Milman. It's counterpart, the Euclidean localisation is extensively studied and has been put to grea…
A Lower Bound for the Mahler Volume of Symmetric Convex Sets
Yashar Memarian
The goal of this paper is to present a lower bound for the Mahler volume of at least 4-dimensional symmetric convex bodies. We define a computable dimension dependent constant thro…
Measure Concentration and the Topology of Positively-Curved Riemannian Manifolds
Yashar Memarian
In this paper, I shall demonstrate that sufficiently high-dimensional closed positively-curved Riemannian manifolds are either diffeomorphic to a spherical space form, or isometric…
A Note on the Geometry of Positively-Curved Riemannian Manifolds
Yashar Memarian
In this paper I present a comparison theorem for the waist of Riemannian manifolds with positive sectional curvature. The main theorem of this paper gives a partial positive answer…
On a Correlation Inequality for Cauchy Type Measures
Yashar Memarian
In this paper we present a correlation inequality with respect to Cauchy type measures. To prove our inequality, we transport the problem onto the Riemannian sphere then state and…
A Geometric Approach to Radial Correlation Type Problems
Yashar Memarian
A radial probability measure is a probability measure with a density (with respect to the Lebesgue measure) which depends only on the distances to the origin. Consider the Euclidea…
A Lower Bound on the Waist of Unit Spheres of Uniformly Convex Normed Spaces
Yashar Memarian
In this paper we give a lower bound on the waist of the unit sphere of a uniformly convex normed space by using the localization technique in codimension greater than one and a str…
On Gromov's Waist of the Sphere Theorem
Yashar Memarian
The goal of this paper is to give a detailed and complete proof of M. Gromov's waist of the sphere theorem.
On the Maximum Number of Vertices of Critically Embedded Graphs
Yashar Memarian
Define a boundary point of a graph which is embedded in the Euclidean plane a vertex which is incident to only one edge. In this paper we consider graphs which are embedded in the…