Differential complexes and exterior calculus (2006)
In this paper we present a new theory of calculus over $k$-dimensional domains in a smooth $n$-manifold, unifying the discrete, exterior, and continuum theories. The calculus begins at a single point...
Lectures on chainlet geometry - new topological methods in geometric measure theory (2005)
These draft notes are from a graduate course given by the author in Berkeley during the spring semester of 2005. They cover the basic ideas of a new, geometric approach to geometric measure theory....
Ravello lecture notes on geometric calculus -- Part I (2004)
In these notes of lectures at the 2004 Summer School of Mathematical Physics in Ravello, Italy, the author develops an approach to calculus in which more efficient choices of limits are taken at key...
Geometric Hodge Star Operator with Applications to the Theorems of Gauss and Green (2004)
The classical divergence theorem for an $n$-dimensional domain $A$ and a smooth vector field $F$ in $n$-space $$\int_{\partial A} F \cdot n = \int_A div F$$ requires that a normal vector field $n(p)$...
On Plateau's Problem for Soap Films with a Bound on Energy (2004)
We prove existence and a.e. regularity of an area minimizing soap film with a bound on energy spanning a given Jordan curve in R^3. The energy of a film is defined to be the sum of its surface area...
Cartan's Magic Formula and Soap Film Structures (2004)
A soap film is actually a thin solid fluid bounded by two surfaces of opposite orientation. It is natural to model the film using one polyhedron for each side. Two problems are to get the polyhedra...
Sandro Buoncristiano: Sheaves of coefficients for homology theories (1998)
Colin Rourke Dob, At Nice, Jenny Harrison, Solution Denjoy, Colin Rourke Bibliography, Nigel Evans Racks, ...
Citations 542 citations in the period 1981–1998 (source BIDS) Successful Ph.D. Students
Stokes' theorem for nonsmooth chains (1993)
Much of the vast literature on the integral during the last two centuries concerns extending the class of integrable functions. In contrast, our viewpoint is akin to that taken by Hassler Whitney...
Research report (B.R.P.)--Massey University, 1990.