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1. CJM 2013 (vol 66 pp. 903)
Non-tame Mice from Tame Failures of the Unique Branch Hypothesis In this paper, we show that the failure of the unique branch
hypothesis (UBH) for tame trees
implies that in some homogenous generic extension of $V$ there is a
transitive model $M$ containing $Ord \cup \mathbb{R}$ such that
$M\vDash \mathsf{AD}^+ + \Theta \gt \theta_0$. In particular, this
implies the existence (in $V$) of a non-tame mouse. The results of
this paper significantly extend J. R. Steel's earlier results
for tame trees.
Keywords:mouse, inner model theory, descriptive set theory, hod mouse, core model induction, UBH Categories:03E15, 03E45, 03E60 |
2. CJM 2012 (vol 66 pp. 197)
On Hyperbolicity of Domains with Strictly Pseudoconvex Ends This article establishes a sufficient condition for Kobayashi
hyperbolicity of unbounded domains in terms of curvature.
Specifically, when $\Omega\subset{\mathbb C}^{n}$ corresponds to a
sub-level set of a smooth, real-valued function $\Psi$, such that the
form $\omega = {\bf i}\partial\bar{\partial}\Psi$ is KÃ¤hler and
has bounded curvature outside a bounded subset, then this domain
admits a hermitian metric of strictly negative holomorphic sectional
curvature.
Keywords:Kobayashi-hyperbolicity, KÃ¤hler metric, plurisubharmonic function Categories:32Q45, 32Q35 |
3. CJM 2008 (vol 60 pp. 822)
Maximum Principles for Subharmonic Functions Via Local Semi-Dirichlet Forms Maximum principles for subharmonic
functions in the framework of quasi-regular local semi-Dirichlet
forms admitting lower bounds are presented.
As applications, we give
weak and strong maximum principles
for (local) subsolutions of a second order elliptic
differential operator on the domain of Euclidean space under conditions on coefficients,
which partially generalize the results by Stampacchia.
Keywords:positivity preserving form, semi-Dirichlet form, Dirichlet form, subharmonic functions, superharmonic functions, harmonic functions, weak maximum principle, strong maximum principle, irreducibility, absolute continuity condition Categories:31C25, 35B50, 60J45, 35J, 53C, 58 |
4. CJM 2005 (vol 57 pp. 506)
Reverse Hypercontractivity for Subharmonic Functions Contractivity and hypercontractivity properties of semigroups
are now well understood when the generator, $A$, is a Dirichlet form
operator.
It has been shown that in some holomorphic function spaces the
semigroup operators, $e^{-tA}$, can be bounded {\it below} from
$L^p$ to $L^q$ when $p,q$ and $t$ are suitably related.
We will show that such lower boundedness occurs also in spaces
of subharmonic functions.
Keywords:Reverse hypercontractivity, subharmonic Categories:58J35, 47D03, 47D07, 32Q99, 60J35 |
5. CJM 2004 (vol 56 pp. 225)
Complex Uniform Convexity and Riesz Measure The norm on a Banach space gives rise to a subharmonic function on the
complex plane for which the distributional Laplacian gives a Riesz measure.
This measure is calculated explicitly here for Lebesgue $L^p$ spaces and the
von~Neumann-Schatten trace ideals. Banach spaces that are $q$-uniformly
$\PL$-convex in the sense of Davis, Garling and Tomczak-Jaegermann are
characterized in terms of the mass distribution of this measure. This gives
a new proof that the trace ideals $c^p$ are $2$-uniformly $\PL$-convex for
$1\leq p\leq 2$.
Keywords:subharmonic functions, Banach spaces, Schatten trace ideals Categories:46B20, 46L52 |