منابع مشابه
Geometric Interpretation of Half-Plane Capacity
Abstract Schramm-Loewner Evolution describes the scaling limits of interfaces in certain statistical mechanical systems. These interfaces are geometric objects that are not equipped with a canonical parametrization. The standard parametrization of SLE is via half-plane capacity, which is a conformal measure of the size of a set in the reference upper half-plane. This has useful harmonic and com...
متن کاملA Geometric Interpretation of Half-Plane Capacity
Let A be a bounded, relatively closed subset of the upper half plane H whose complement in H is simply connected. If Bt is a standard complex Brownian motion and τA = inf{t ≥ 0 : Bt 6∈ H \A}, the half-plane capacity hcap(A) is defined as hcap(A) := lim y→∞ y E [Im(BτA)] . This quantity arises in the study of Schramm-Loewner Evolutions (SLE). In this note, we show that hcap(A) is comparable to a...
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Exact solutions of conformal turbulence restricted on a upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus in the presence of an anisotropic boundary, these exact solutions of turbulence generalize Kolmogorov’s solution consistently and differ from the Polyakov’s...
متن کاملScreen conformal half-lightlike submanifolds
We study some properties of a half-lightlike submanifoldM , of a semi-Riemannianmanifold, whose shape operator is conformal to the shape operator of its screen distribution. We show that any screen distribution S(TM) of M is integrable and the geometry of M has a close relation with the nondegenerate geometry of a leaf of S(TM). We prove some results on symmetric induced Ricci tensor and null s...
متن کاملPlane Strain Deformation of a Poroelastic Half-Space Lying Over Another Poroelastic Half-Space
The plane strain deformation of an isotropic, homogeneous, poroelastic medium caused by an inclined line-load is studied using the Biot linearized theory for fluid saturated porous materials. The analytical expressions for the displacements and stresses in the medium are obtained by applying suitable boundary conditions. The solutions are obtained analytically for the limiting case of undrained...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2013
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2013-11811-3