A quantitative isoperimetric inequality on the sphere

2017 ◽  
Vol 10 (3) ◽  
pp. 223-265 ◽  
Author(s):  
Verena Bögelein ◽  
Frank Duzaar ◽  
Nicola Fusco

AbstractIn this paper we prove a quantitative version of the isoperimetric inequality on the sphere with a constant independent of the volume of the set E.

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Annalisa Cesaroni ◽  
Matteo Novaga

AbstractWe show a quantitative version of the isoperimetric inequality for a non local perimeter of Minkowski type. We also apply this result to study isoperimetric problems with repulsive interaction terms, under volume and convexity constraints.We prove existence of minimizers, and we describe their shape as the volume tends to zero or to infinity.


Author(s):  
G. Cliff ◽  
M.J. Nasir ◽  
G.W. Lorimer ◽  
N. Ridley

In a specimen which is transmission thin to 100 kV electrons - a sample in which X-ray absorption is so insignificant that it can be neglected and where fluorescence effects can generally be ignored (1,2) - a ratio of characteristic X-ray intensities, I1/I2 can be converted into a weight fraction ratio, C1/C2, using the equationwhere k12 is, at a given voltage, a constant independent of composition or thickness, k12 values can be determined experimentally from thin standards (3) or calculated (4,6). Both experimental and calculated k12 values have been obtained for K(11<Z>19),kα(Z>19) and some Lα radiation (3,6) at 100 kV. The object of the present series of experiments was to experimentally determine k12 values at voltages between 200 and 1000 kV and to compare these with calculated values.The experiments were carried out on an AEI-EM7 HVEM fitted with an energy dispersive X-ray detector.


Author(s):  
Brian Street

This book develops a new theory of multi-parameter singular integrals associated with Carnot–Carathéodory balls. The book first details the classical theory of Calderón–Zygmund singular integrals and applications to linear partial differential equations. It then outlines the theory of multi-parameter Carnot–Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. The book then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. This book will interest graduate students and researchers working in singular integrals and related fields.


Sign in / Sign up

Export Citation Format

Share Document