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pro vyhledávání: '"Lawson JR"'
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
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
We present a general framework for obtaining currential double transgression formulas on complex manifolds which can be seen as manifestations of Bott-Chern Duality. These results complement on one hand the simple transgression formulas obtained by H
Externí odkaz:
http://arxiv.org/abs/2003.14326
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