Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and Convergence of the Sasaki-Ricci Flow   We introduce a holomorphic sheaf E on a Sasaki manifold and study two new
notions of stability for E along the Sasaki-Ricci flow related to the `jumping
up' of the number of global holomorphic sections of E at infinity. First, we
show that if the Mabuchi K-energy is bounded below, the transverse Riemann
tensor is bounded in C^{0} along the flow, and the C -infinity closure of the
Sasaki structure under the diffeomorphism group does not contain a Sasaki
structure with strictly more global holomorphic sections of E, then the
Sasaki-Ricci flow converges exponentially fast to a Sasaki-Einstein metric.
Secondly, we show that if the Futaki invariant vanishes, and the lowest
positive eigenvalue of the d-bar Laplacian on global sections of E is bounded
away from zero uniformly along the flow, then the Sasaki-Ricci flow converges
exponentially fast to a Sasaki-Einstein metric.

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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg