3 problems

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Burns's conjecture on entire Grauert tubes
Let $(M,g)$ be a real-analytic Riemannian manifold, and let $T^\infty M:=TM$ be an entire Grauert tube, meaning that the tangent bundle admits a Stein structure with strictly pluri…
Conjectureopenaffine-varieties complex-geometry grauert-tubesarXiv posted 2 days ago
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Maximal holomorphic extension of eigenfunctions to Grauert tubes
Maximal extension conjecture. All eigenfunctions extend holomorphically to the maximal Grauert tube $M_{\tau_g}$ .
Conjectureopencomplex-analysis eigenfunctions grauert-tubesarXiv posted 2 days ago
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Equality of the geometric and analytic Grauert tube radii
Equality conjecture. The two radii should be equal:
Conjectureopencomplex-geometry grauert-tubes spectral-theoryarXiv posted 2 days ago

Burns's conjecture on entire Grauert tubes