Category: Integral geometry

Penrose transform
In theoretical physics, the Penrose transform, introduced by Roger Penrose , is a complex analogue of the Radon transform that relates on spacetime to cohomology of sheaves on complex projective space
Funk transform
In the mathematical field of integral geometry, the Funk transform (also known as Minkowski–Funk transform, Funk–Radon transform or spherical Radon transform) is an integral transform defined by integ
Stochastic geometry
In mathematics, stochastic geometry is the study of random spatial patterns. At the heart of the subject lies the study of random point patterns. This leads to the theory of spatial point processes, h
X-ray transform
In mathematics, the X-ray transform (also called John transform) is an integral transform introduced by Fritz John in 1938 that is one of the cornerstones of modern integral geometry. It is very close
Radon transform
In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value a
Euler calculus
Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently by integrating with respect to the Euler characteristic
Institute of Mathematics of National Academy of Sciences of Armenia
The Institute of Mathematics of National Academy of Sciences of Armenia (Armenian: Հայաստանի ԳԱԱ մաթեմատիկայի ինստիտուտ) is owned and operated by the Armenian Academy of Sciences, located in Yerevan.
Hadwiger's theorem
In integral geometry (otherwise called geometric probability theory), Hadwiger's theorem characterises the valuations on convex bodies in It was proved by Hugo Hadwiger.
Buffon's noodle
In geometric probability, the problem of Buffon's noodle is a variation on the well-known problem of Buffon's needle, named after Georges-Louis Leclerc, Comte de Buffon who lived in the 18th century.
Pompeiu problem
In mathematics, the Pompeiu problem is a conjecture in integral geometry, named for Dimitrie Pompeiu, who posed the problem in 1929, as follows. Suppose f is a nonzero continuous function defined on a
Mixed volume
In mathematics, more specifically, in convex geometry, the mixed volume is a way to associate a non-negative number to an -tuple of convex bodies in -dimensional space. This number depends on the size
Crofton formula
In mathematics, the Crofton formula, named after Morgan Crofton (1826–1915), is a classic result of integral geometry relating the length of a curve to the expected number of times a "random" line int
Buffon's needle problem
In mathematics, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon: Suppose we have a floor made of parallel strips of wood, each the same
Mean width
In geometry, the mean width is a measure of the "size" of a body; see Hadwiger's theorem for more about the available measures of bodies. In dimensions, one has to consider -dimensional hyperplanes pe
Bateman transform
In the mathematical study of partial differential equations, the Bateman transform is a method for solving the Laplace equation in four dimensions and wave equation in three by using a line integral o
Integral geometry
In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a v
Borell–Brascamp–Lieb inequality
In mathematics, the Borell–Brascamp–Lieb inequality is an integral inequality due to many different mathematicians but named after , and Elliott Lieb. The result was proved for p > 0 by Henstock and M
Prékopa–Leindler inequality
In mathematics, the Prékopa–Leindler inequality is an integral inequality closely related to the , the Brunn–Minkowski inequality and a number of other important and classical inequalities in analysis
Holmes–Thompson volume
In geometry of normed spaces, the Holmes–Thompson volume is a notion of volume that allows to compare sets contained in different normed spaces (of the same dimension). It was introduced by Raymond D.