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JP Journal of Geometry and Topology

JP Journal of Geometry and Topology
Volume 7, Issue 1, Pages 1 - 22 (March 2007)

INTEGRAL REPRESENTATIONS OF SOLUTIONS TO THE SUB-LAPLACE EQUATIONS BY TWISTOR THEORY Yoshinori Machida (Japan) Received September 14, 2006 References:
[1] K. Aomoto and Y. Machida, Twistor integral representations of fundamental solutions of massless field equations, J. Geometry and Physics 32 (1999), 189-210. [2] G. B. Folland, A fundamental solution for a subelliptic operator, Bull. Amer. Math. Soc. 79 (1973), 373-376. [3] G. B. Folland and E. M. Stein, Estimates for the complex and analysis on the Heisenberg group, Commun. Pure Appl. Math. 27 (1974), 429-522. [4] E. L. Grinberg, On images of Radon transforms, Duke Math. J. 52 (1985), 939-972. [5] E. L. Grinberg, Euclidean Radon transforms: ranges and restrictions, Contemporary Math. 63 (1987), 109-133. [6] F. John, The ultrahyperbolic differential equation with four independent variables, Duke Math. J. 4 (1938), 300-322.

Keywords and phrases: sub-Laplacian, sub-Riemannian geometry, Heisenberg group, contact structure, twistor theory.

Communicated by Johann Davidov