82 citations · 224 across the 16 of their papers we have counts for
20 papers
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…
An extension of Alexandrov's theorem on second derivatives of convex functions
Joseph H. G. Fu
If is a function of variables that is locally approximable by a sequence of smooth functions satisfying local bounds on the determinants of the minors of the He…
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…
Theory of valuations on manifolds, III. Multiplicative structure in the general case
Semyon Alesker, Joseph H. G. Fu
This article is the third part of the series of articles where the theory of valuations on manifolds is constructed. In math.MG/0503399 the notion of a smooth valuation on a manifo…
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…
Circles Minimize most Knot Energies
Aaron Abrams, Jason Cantarella, Joseph H. G. Fu +2
We define a new class of knot energies (known as renormalization energies) and prove that a broad class of these energies are uniquely minimized by the round circle. Most of O'Hara…
On fine differentiability properties of horizons and applications to Riemannian geometry
P. T. Chrusciel, J. H. G. Fu, G. J. Galloway +1
We study fine differentiability properties of horizons. We show that the set of end points of generators of a n-dimensional horizon H (which is included in a (n+1)-dimensional spac…
Stiefel-Whitney Classes and the Conormal Cycle of a Singular Variety
Joseph H. G. Fu, Clint McCrory
A geometric construction of Sullivan's Stiefel-Whitney homology classes of a real analytic variety is given by means of the conormal cycle of an embedding of in a smooth va…