Abstract
In this short note, we discuss the monotonicity of the eigen-values of the Laplacian operator to the Ricci-Hamilton flow on a compact or a complete non-compact Riemannian manifold. We show that the eigenvalue of the Lapacian operator on a compact domain associated with the evolving Ricci flow is non-decreasing provided the scalar curvature having a non-negative lower bound and Einstein tensor being not too negative. This result will be useful in the study of blow-up models of the Ricci-Hamilton flow.
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Mathematics Subject Classifications (1991): 53C44
In Memory of S.S. Chern
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Ma, L. Eigenvalue Monotonicity for the Ricci-Hamilton Flow. Ann Glob Anal Geom 29, 287–292 (2006). https://doi.org/10.1007/s10455-006-9018-8
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DOI: https://doi.org/10.1007/s10455-006-9018-8