Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Lichnerowicz and Obata first eigenvalue theorems and the Obata
  uniqueness result in the Yamabe problem on CR and quaternionic contact
  manifolds   We report on some aspects and recent progress in certain problems in the
sub-Riemannian CR and quaternionic contact (QC) geometries. The focus are the
corresponding Yamabe problems on the round spheres, the Lichnerowicz-Obata
first eigenvalue estimates, and the relation between these two problems. A
motivation from the Riemannian case highlights new and old ideas which are then
developed in the settings of Iwasawa sub-Riemannian geometries.

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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex