Equivariant asymptotics on Grauert tubes
Simone Gallivanone1; Roberto Paoletti1
1 Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, Via R. Cozzi 55, 20125 Milano, Italy
Mathematics Research Reports, Volume 6 (2025), pp. 51-61.

We report on recent work on the scaling asymptotics of the equivariant components of Poisson and Szegö kernels on the Grauert tube boundaries associated to a real-analytic Riemannian manifold acted upon by a compact Lie group. Building largely on techniques of Zelditch and Chang and Rabinowitz, we describe the asymptotic concentration along the zero locus of the moment map of the equivariant eigenfunctions of a Toeplitz operator associated to the homogeneous geodesic flow and of the complexified equivariant eigenfunctions of the Laplacian. We also digress on some applications.

Received:
Revised:
Published online:
DOI: 10.5802/mrr.23
Classification: 34L10, 34L20, 32D15, 32M05, 32T25, 53D25
Keywords: Riemannian manifold, geodesic flow, Grauert tubes, complexified eigenfunctions, Poisson-wave operators, CR structure, Szegő kernel, Hamiltonian Lie group actions, moment maps, isotypical components, scaling asymptotics

Simone Gallivanone 1; Roberto Paoletti 1

1 Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, Via R. Cozzi 55, 20125 Milano, Italy
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Simone Gallivanone; Roberto Paoletti. Equivariant asymptotics on Grauert tubes. Mathematics Research Reports, Volume 6 (2025), pp. 51-61. doi : 10.5802/mrr.23. https://mrr.centre-mersenne.org/articles/10.5802/mrr.23/

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