arXiv subjects
Publications and source records attributed to Carto Wong.
We prove that for almost every Brownian motion sample, the corresponding SLE(κ) curves parameterized by capacity exist and change continuously in the supremum norm when κvaries in the interval [0,κ_0), where κ_0=8(2-\sqrt{3})=2.143... We estimate the κ-dependent modulus of continuity of the curves and also give an estimate on the modulus of continuity for the supremum norm change with κ.
In this paper, we show that the chordal Loewner differential equation with $C^β$ driving function generates a $C^{β+ 1/2}$ slit for $1/2 < β\leq 2$, except when $β= 3/2$ the slit is only proved to be weakly $C^{1,1}$.
In this note, we show that the half-plane capacity of a subset of the upper half-plane is comparable to a simple geometric quantity, namely the euclidean area of the hyperbolic neighborhood of radius one of this set. This is achieved by proving a similar estimate for the conformal radius of a subdomain of the unit disc, and by establishing a simple relation between these two quantities.