Zobrazeno 1 - 10
of 3 228
pro vyhledávání: '"Harvey, F. A."'
Autor:
Harvey, F. Reese, Lawson Jr, H. Blaine
Let ${\mathfrak g}$ be a Garding-Dirichlet operator on the set S(n) of symmetric $n\times n$ matrices. We assume that ${\mathfrak g}$ is $I$-central, that is, $D_I {\mathfrak g} = k I$ for some $k>0$. Then $$ {\mathfrak g}(A)^{1\over N} \ \geq\ {\mat
Externí odkaz:
http://arxiv.org/abs/2407.05408
Autor:
Harvey, F. Reese, Lawson Jr, H. Blaine
The objective of this note is to establish the Determinant Majorization Formula $F(A)^{1\over N} \geq \det(A)^{1\over n}$ for all operators $F$ determined by an invariant Garding-Dirichlet polynomial of degree $N$ on symmetric $n \times n$ matrices.
Externí odkaz:
http://arxiv.org/abs/2207.01729
Autor:
Harvey, F. Reese, Payne, Kevin R.
We discuss one of the many topics that illustrate the interaction of Blaine Lawson's deep geometric and analytic insights. The first author is extremely grateful to have had the pleasure of collaborating with Blaine over many enjoyable years. The top
Externí odkaz:
http://arxiv.org/abs/2203.14015
Autor:
Silver, Harvey F.1, Boutz, Abigail L.2
Publikováno v:
Educational Leadership. Summer2024, Vol. 81 Issue 9, p54-59. 6p.
We prove comparison principles for nonlinear potential theories in euclidian spaces in a very straightforward manner from duality and monotonicity. We shall also show how to deduce comparison principles for nonlinear differential operators, a program
Externí odkaz:
http://arxiv.org/abs/2009.01611
This note adapts the sophisticated Richberg technique for approximation in pluripotential theory to the $F$-potential theory associated to a general nonlinear convex subequation $F \subset J^2(X)$ on a manifold $X$. The main theorem is the following
Externí odkaz:
http://arxiv.org/abs/2005.04033
Autor:
Harvey, F. Reese, Lawson Jr, H. Blaine
The Special Lagrangian Potential Equation for a function $u$ on a domain $\Omega\subset {\bf R}^n$ is given by ${\rm tr}\{\arctan(D^2 \,u) \} = \theta$ for a contant $\theta \in (-n {\pi\over 2}, n {\pi\over 2})$. For $C^2$ solutions the graph of $Du
Externí odkaz:
http://arxiv.org/abs/2001.09818
Autor:
Harvey, F. Reese, Lawson Jr, H. Blaine
We introduce and investigate the notion of a `generalized equation' of the form $f(D^2 u)=0$, based on the notions of subequations and Dirichlet duality. Precisely, a subset ${{\mathbb H}}\subset {\rm Sym}^2({\mathbb R}^n)$ is a generalized equation
Externí odkaz:
http://arxiv.org/abs/1901.07093
Autor:
Harvey, F. Reese, Lawson Jr, H. Blaine
We shall discuss the inhomogeneous Dirichlet problem for: $f(x,u, Du, D^2u) = \psi(x)$ where $f$ is a "natural" differential operator, with a restricted domain $F$, on a manifold $X$. By "natural" we mean operators that arise intrinsically from a giv
Externí odkaz:
http://arxiv.org/abs/1805.11121
Autor:
Harvey, F. Reese, Lawson Jr, H. Blaine
Publikováno v:
Surveys in Differential Geometry, Vol. 22, No. 1 (2017), pp. 217-257
The purpose of this paper is to establish a Lagrangian potential theory, analogous to the classical pluripotential theory, and to define and study a Lagrangian differential operator of Monge-Ampere type. This development is new even in ${\bf C}^n$. H
Externí odkaz:
http://arxiv.org/abs/1712.03525