A spherical rearrangement proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem

We prove the stability of the ball as global minimizer of an attractive shape functional under volume constraint, by means of mass transportation arguments. The stability exponent is $1/2$ and it is sharp. Moreover, we use such stability result together with the quantitative (possibly fractional) isoperimetric inequality to prove that the ball is a global minimizer of a shape functional involving both an attractive and a repulsive term with a sufficiently large fixed volume and with a suitable (possibly fractional) perimeter penalization.

Analysis on Trees with Nondoubling Flow Measures

We consider trees with root at infinity endowed with flow measures, which are nondoubling measures of at least exponential growth and which do not satisfy the isoperimetric inequality. In this setting, we develop a Calderón–Zygmund theory and we define BMO and Hardy spaces, proving a number of desired results extending the corresponding theory as known in more classical settings.

17 Essays On Modern Physics: From Sonoluminescence To Superconductivity

Physics is beautiful & amazing. This paper contains 17 easy-to-read essays on modern physics over various aspects that can easily manifest a curiosity in the young minds. Essays are there without any math which entails for a easier read. They are, Complexity of Physical Law In Unification, Levitation Using Superconductivity, Cryogenics, Nuclear Energies, Speed of The Sound, To Travel In Time Is To Travel In Space, Restricted 3-Body Problem of Mechanics, Sonoluminescence, Acoustic Levitation, Evolution & Physics, 11-Dimensional Super-Gravity, Black Hole Titbits, Frequency & Wavelength (Å), Investigating The Possible shapes Of The Universe, Chaos & Unpredictability, Cat’s Schrodinger, Isoperimetric Inequality.

A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs

We study in this paper the relationship of isoperimetric inequality and hyperbolicity for graphs and Riemannian manifolds. We obtain a characterization of graphs and Riemannian manifolds (with bounded local geometry) satisfying the (Cheeger) isoperimetric inequality, in terms of their Gromov boundary, improving similar results from a previous work. In particular, we prove that having a pole is a necessary condition to have isoperimetric inequality and, therefore, it can be removed as hypothesis.