TL;DR
This paper proves that the Hausdorff measure of SLE curves is zero at a specific dimension related to the parameter , providing insight into the fractal geometry of these stochastic curves.
Contribution
The paper establishes that the Hausdorff measure of SLE curves is zero at the critical dimension d = 1 + /8, advancing understanding of their fractal properties.
Findings
Hausdorff measure of SLE curves is zero at the critical dimension
Provides rigorous proof for measure properties of SLE curves
Enhances understanding of fractal geometry in stochastic processes
Abstract
In this paper we prove that the Hausdorff d-measure of SLE_{\kappa} is zero when d = 1+{\kappa}/ 8 .
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