First eigenvalues of geometric operators under the Yamabe flow

  • Pak Tung Ho


Suppose \((M,g_0)\) is a compact Riemannian manifold without boundary of dimension \(n\ge 3\). Using the Yamabe flow, we obtain estimate for the first nonzero eigenvalue of the Laplacian of \(g_0\) with negative scalar curvature in terms of the Yamabe metric in its conformal class. On the other hand, we prove that the first eigenvalue of some geometric operators on a compact Riemannian manifold is nondecreasing along the unnormalized Yamabe flow under suitable curvature assumption. Similar results are obtained for manifolds with boundary and for CR manifold.


Yamabe flow Eigenvalue CR manifold 

Mathematics Subject Classification

Primary 53C44 58C40 Secondary 35K55 53C21 58J35 


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Authors and Affiliations

  1. 1.Department of MathematicsSogang UniversitySeoulKorea

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