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A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities
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Burkhard Wilking
Published/Copyright:
March 6, 2012
Abstract
We consider a subset S of the complex Lie algebra 𝔰𝔬 (n, ℂ) and the cone C (S) of curvature operators which are nonnegative on S. We show that C (S) defines a Ricci flow invariant curvature condition if S is invariant under AdSO (n, ℂ). The analogue for Kähler curvature operators holds as well. Although the proof is very simple and short, it recovers all previously known invariant nonnegativity conditions. As an application we reprove that a compact Kähler manifold with positive orthogonal bisectional curvature evolves to a manifold with positive bisectional curvature and is thus biholomorphic to ℂℙn. Moreover, the methods can also be applied to prove Harnack inequalities.
Received: 2011-06-10
Published Online: 2012-03-06
Published in Print: 2013-06
©[2013] by Walter de Gruyter Berlin Boston
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- Higher Kronecker “limit” formulas for real quadratic fields
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- The Taylor–Wiles method for coherent cohomology
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- A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities
Articles in the same Issue
- Classification of surfaces of general type with Euler number 3
- Higher Kronecker “limit” formulas for real quadratic fields
- The u-invariant of p-adic function fields
- The composition Hall algebra of a weighted projective line
- The Taylor–Wiles method for coherent cohomology
- The space of Heegaard splittings
- Wach modules and critical slope p-adic L-functions
- Algebraic varieties with quasi-projective universal cover
- A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities
