Geodesic
The Loewner differential equation and slit mappings
Marshall, Donald1 ; Rohde, Steffen1
1 Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
Journal of the American Mathematical Society, Tome 18 (2005) no. 4, pp. 763-778

Voir la notice de l'article provenant de la source American Mathematical Society

We show that the Loewner equation generates slits if the driving term is Hölder continuous with exponent 1/2 and small norm and that this is best possible.
DOI : 10.1090/S0894-0347-05-00492-3

Marshall, Donald 1 ; Rohde, Steffen 1

1 Department of Mathematics, University of Washington, Seattle, Washington 98195-4350 
@article{10_1090_S0894_0347_05_00492_3,
     author = {Marshall, Donald and Rohde, Steffen},
     title = {The {Loewner} differential equation and slit mappings},
     journal = {Journal of the American Mathematical Society},
     pages = {763--778},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2005},
     doi = {10.1090/S0894-0347-05-00492-3},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-05-00492-3/}
}
TY  - JOUR
AU  - Marshall, Donald
AU  - Rohde, Steffen
TI  - The Loewner differential equation and slit mappings
JO  - Journal of the American Mathematical Society
PY  - 2005
SP  - 763
EP  - 778
VL  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-05-00492-3/
DO  - 10.1090/S0894-0347-05-00492-3
ID  - 10_1090_S0894_0347_05_00492_3
ER  - 
%0 Journal Article
%A Marshall, Donald
%A Rohde, Steffen
%T The Loewner differential equation and slit mappings
%J Journal of the American Mathematical Society
%D 2005
%P 763-778
%V 18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-05-00492-3/
%R 10.1090/S0894-0347-05-00492-3
%F 10_1090_S0894_0347_05_00492_3
Marshall, Donald; Rohde, Steffen. The Loewner differential equation and slit mappings. Journal of the American Mathematical Society, Tome 18 (2005) no. 4, pp. 763-778. doi: 10.1090/S0894-0347-05-00492-3

[1] Ahlfors, Lars V. Lectures on quasiconformal mappings 1966

[2] De Branges, Louis A proof of the Bieberbach conjecture Acta Math. 1985 137 152

[3] Carleson, L., Makarov, N. Aggregation in the plane and Loewner’s equation Comm. Math. Phys. 2001 583 607

[4] Earle, Clifford J., Epstein, Adam Lawrence Quasiconformal variation of slit domains Proc. Amer. Math. Soc. 2001 3363 3372

[5] Duren, Peter L. Univalent functions 1983

[6] Fernã¡Ndez, Josã© L., Heinonen, Juha, Martio, Olli Quasilines and conformal mappings J. Analyse Math. 1989 117 132

[7] Gehring, Frederick W. Characteristic properties of quasidisks 1982 97

[8] Kufarev, P. P. A remark on integrals of Löwner’s equation Doklady Akad. Nauk SSSR (N.S.) 1947 655 656

[9] Kã¼Hnau, R. Numerische Realisierung konformer Abbildungen durch “Interpolation” Z. Angew. Math. Mech. 1983 631 637

[10] Lawler, Gregory F., Schramm, Oded, Werner, Wendelin Values of Brownian intersection exponents. I. Half-plane exponents Acta Math. 2001 237 273

[11] Lawler, Gregory F., Schramm, Oded, Werner, Wendelin The dimension of the planar Brownian frontier is 4/3 Math. Res. Lett. 2001 13 23

[12] Lehto, O., Virtanen, K. I. Quasiconformal mappings in the plane 1973

[13] Pommerenke, Christian Univalent functions 1975 376

[14] Pommerenke, Ch. Boundary behaviour of conformal maps 1992

[15] Schramm, Oded Scaling limits of loop-erased random walks and uniform spanning trees Israel J. Math. 2000 221 288

[16] Smirnov, Stanislav Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits C. R. Acad. Sci. Paris Sér. I Math. 2001 239 244

Cité par Sources :