82 citations · 224 across the 16 of their papers we have counts for
15 papers · 1 filter
On the Gaussian Kinematic Formula of R. Adler and J. Taylor
Joseph H. G. Fu
We apply methods of algebraic integral geometry to prove a special case of the Gaussian kinematic formula of Adler-Taylor. The idea, suggested already by Adler and Taylor, is to vi…
The Weyl tube theorem for Kähler manifolds
Andreas Bernig, Joseph H. G. Fu, Gil Solanes +1
As sharpened in terms of Alesker's theory of valuations on manifolds, a classic theorem of Weyl asserts that the coefficients of the tube polynomial of an isometrically embedded ri…
Riemannian curvature measures
Joseph H. G. Fu, Thomas Wannerer
A famous theorem of Weyl states that if is a compact submanifold of euclidean space, then the volumes of small tubes about are given by a polynomial in the radius , with…
Dual curvature measures in hermitian integral geometry
Andreas Bernig, Joseph H. G. Fu, Gil Solanes
The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space of dual unitarily invariant curvatur…
Kinematic formulas for sets defined by differences of convex functions
Joseph H. G. Fu, Dusan Pokorny, Jan Rataj
Two of the authors have defined the class as the class of all subsets of a smooth manifold that may be expressed in local coordinates as certain sublevel sets of DC (…
Intersection theory and the Alesker product
Joseph H. G. Fu
Alesker has introduced the space of {\it smooth valuations} on a smooth manifold , and shown that it admits a natural commutative multiplication. Although…
Piecewise linear approximation of smooth functions of two variables
Joseph H. G. Fu, Ryan C. Scott
Given a piecewise linear (PL) function defined on an open subset of , one may construct by elementary means a unique polyhedron with multiplicities $\D(p)$ in the cotange…
Symmetric Criticality for Tight Knots
Jason Cantarella, Jennifer Ellis, Joseph H. G. Fu +1
We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configu…
Integral geometry of complex space forms
Andreas Bernig, Joseph H. G. Fu, Gil Solanes
We show how Alesker's theory of valuations on manifolds gives rise to an algebraic picture of the integral geometry of any Riemannian isotropic space. We then apply this method to…
Algebraic integral geometry
Joseph H. G. Fu
This is a revised version of the notes from the week-long course I gave at the Centre de Recerca Matematica, Barcelona, in September of 2010. The aim is to give a working overview…
Ropelength Criticality
Jason Cantarella, Joseph H. G. Fu, Robert Kusner +1
The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embedded in Euclidean three-space. The core curve of such a tube is called a tight k…
Hermitian integral geometry
Andreas Bernig, Joseph H. G. Fu
We give in explicit form the principal kinematic formula for the action of the affine unitary group on $\C^n$, together with a straightforward algebraic method for computing the fu…
Convolution of convex valuations
Andreas Bernig, Joseph H. G. Fu
We show that the natural "convolution" on the space of smooth, even, translation-invariant convex valuations on a euclidean space , obtained by intertwining the product and the…
Structure of the unitary valuation algebra
Joseph H. G. Fu
S. Alesker has shown that if is a compact subgroup of O(n) acting transitively on the unit sphere then the vector space of continuous, translation-invariant,…
Criticality for the Gehring link problem
Jason Cantarella, Joseph H G Fu, Rob Kusner +2
In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and…