Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic geometry and the uniqueness of Grauert tubes   A compact real analytic Riemannian manifold M admits a canonical
complexification with plurisubharmonic exhaustion function satisfying the
homogeneous complex Monge-Ampere equation, called a Grauert tube. From the
point of view of complex analysis, several authors have considered whether a
given complex manifold can arise in more than one way from this construction.
We show that given a compact M and a finite exhaustion, the underlying
Riemannian structure is unique. The proof uses the technique of holomorphic
disks spanning two exact Lagrangian submanifolds of the cotangent bundle of M,
and Schwarz reflection.

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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga