# Monotonicity formulas for the ﬁrst eigenvalue of the weighted p-Laplacianunder the Ricci-harmonic ﬂow

- Post by: yusuff
- September 2, 2020
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Let p,φbe the weighted p-Laplacian deﬁned on a smooth metric measure space.We study the evolution and monotonicity formulas for the ﬁrst eigenvalue,λ1=λ(p,φ), of p,φunder the Ricci-harmonic ﬂow. We derive some monotonicquantities involving the ﬁrst eigenvalue, and as a consequence, this shows that λ1ismonotonically nondecreasing and almost everywhere diﬀerentiable along the ﬂowexistence

https://eprints.lmu.edu.ng/id/eprint/2312

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