A Sharp Condition for the Loewner Equation to Generate Slits

By Joan Lind. 2003

82 citations recorded by the source corpus.

D. Marshall and S. Rohde have recently shown that there exists C 0 > 0 so that the Loewner equation generates slits whenever the driving term is Holder continuous with exponent ½ and norm less than C 0 [11]. In this paper, we show that the maximal value for C 0 is 4.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1c5adaffd548b6f640120d1e6fd04e9d31aae08d

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

The evolution of Loewner's differential equations (2010, unknown): “Rhode [42], [39], [40].”
The Loewner differential equation and slit mappings (2005, background): “Update. After this paper was submitted, Joan Lind [ 12 ] proved that the unspecified constant C in Theorem 1.1 is C = 4, and that this is best possible.”
The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$ (2016, background): “Lind [16] derived the following sharp condition for a driving function to generate a quasislit halfplane in the chordal setting, i.”
Loewner chains in the unit disk (2009, background): “Some recent developments concerning the relationship between properties of the driving term and the geometry of solutions to (1.4) and (1.5) can be found in [ 19 , 26, 30].”