Levi equation and evolution of subsets of C 2

Zbigniew Slodkowski; Giuseppe Tomassini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1996)

  • Volume: 7, Issue: 4, page 235-239
  • ISSN: 1120-6330

Abstract

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In this Note we state some results obtained studying the evolution of compact subsets of C 2 by Levi curvature. This notion appears to be the natural extension to Complex Analysis of the notion of evolution by mean curvature.

How to cite

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Slodkowski, Zbigniew, and Tomassini, Giuseppe. "Levi equation and evolution of subsets of \( \mathbf{C}^{2} \)." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.4 (1996): 235-239. <http://eudml.org/doc/244319>.

@article{Slodkowski1996,
abstract = {In this Note we state some results obtained studying the evolution of compact subsets of \( \mathbf\{C\}^\{2\} \) by Levi curvature. This notion appears to be the natural extension to Complex Analysis of the notion of evolution by mean curvature.},
author = {Slodkowski, Zbigniew, Tomassini, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Pseudoconvex domains; Real submanifolds in complex manifolds; Parabolic equations and systems; Levi equation; evolution of subsets of ; pseudoconvex domains; real submanifolds in complex manifolds; parabolic equations and systems},
language = {eng},
month = {12},
number = {4},
pages = {235-239},
publisher = {Accademia Nazionale dei Lincei},
title = {Levi equation and evolution of subsets of \( \mathbf\{C\}^\{2\} \)},
url = {http://eudml.org/doc/244319},
volume = {7},
year = {1996},
}

TY - JOUR
AU - Slodkowski, Zbigniew
AU - Tomassini, Giuseppe
TI - Levi equation and evolution of subsets of \( \mathbf{C}^{2} \)
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/12//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 4
SP - 235
EP - 239
AB - In this Note we state some results obtained studying the evolution of compact subsets of \( \mathbf{C}^{2} \) by Levi curvature. This notion appears to be the natural extension to Complex Analysis of the notion of evolution by mean curvature.
LA - eng
KW - Pseudoconvex domains; Real submanifolds in complex manifolds; Parabolic equations and systems; Levi equation; evolution of subsets of ; pseudoconvex domains; real submanifolds in complex manifolds; parabolic equations and systems
UR - http://eudml.org/doc/244319
ER -

References

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  1. CRANDALL, M. G. - LIONS, P.-L., Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc., 277, 1983, 1-42. Zbl0599.35024MR690039DOI10.2307/1999343
  2. EVANS, L. C., A convergence theorem for solutions of nonlinear second order elliptic equations. Indiana Univ. Math. J., 27, 1978, 875-887. Zbl0408.35037MR503721DOI10.1512/iumj.1978.27.27059
  3. EVANS, L. C. - SPRUCK, J., Motion of level sets by mean curvature. I. J. Diff. Geom., 33, 1991, 635-681. Zbl0726.53029MR1100206
  4. GAGE, M. - HAMILTON, R. S., The heat equation shrinking convex plane curves. J. Diff. Geom., 23, 1986, 69-96. Zbl0621.53001MR840401
  5. HUISKEN, G., Flow by mean curvature of convex surfaces into spheres. J. Diff. Geom., 20, 1984, 237-266. Zbl0556.53001MR772132
  6. SLODKOWSKI, Z. - TOMASSINI, G., Geometric properties of solutions of the Levi curvature equation in C 2 . J. Funct. Anal., to appear. Zbl0874.47023MR1391635DOI10.1006/jfan.1996.0061

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