64 citations · 212 across the 30 of their papers we have counts for
10 papers · 1 filter
Geometric plurisubharmonicity and convexity - an introduction
F. Reese Harvey, H. Blaine Lawson
This is an essay on potential theory for geometric plurisubharmonic functions. It begins with a given closed subset G of the Grassmann bundle of tangent -planes to a r…
p-convexity, p-plurisubharmonicity and the Levi problem
F. Reese Harvey, H. Blaine Lawson
Three results in p-convex geometry are established. First is the analogue of the Levi problem in several complex variables, namely: local p-convexity implies global p-convexity. Th…
Split Special Lagrangian Geometry
F. Reese Harvey, H. Blaine Lawson
One purpose of this article is to draw attention to the seminal work of J. Mealy in 1989 on calibrations in semi-riemannian geometry where split SLAG geometry was first introduced.…
Plurisubharmonicity in a General Geometric Context
F. Reese Harvey, H. Blaine Lawson
Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much…
Duality of Positive Currents and Plurisubharmonic Functions in Calibrated Geometry
F. Reese Harvey, H. Blaine Lawson
Recently the authors showed that there is a robust potential theory attached to any calibrated manifold (X,ϕ). In particular, on X there exist ϕ-plurisubharmonic functions, ϕ-conve…
An Introduction to Potential Theory in Calibrated Geometry
F. Reese Harvey, H. Blaine Lawson
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry an…
Lefschetz-Pontrjagin Duality for Differential Characters
F. Reese Harvey, H. Blaine Lawson
A theory of differential characters is developed for manifolds with boundary. This is done from both the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the…
D-bar Sparks, I
F. Reese Harvey, H. Blaine Lawson
A d-bar-analogue of differential characters for complex manifolds is introduced and studied using a new theory of homological spark complexes. Many essentially different spark comp…
Finite volume flows and Morse theory
F. Reese Harvey, H. Blaine Lawson
In this paper we present a new approach to Morse theory based on the de Rham-Federer theory of currents. The full classical theory is derived in a transparent way. The methods carr…
A theory of characteristic currents associated with a singular connection
Reese Harvey, H. Blaine Jr. Lawson
This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth…