Monotonicity of first eigenvalues along the Yamabe flow

Liangdi Zhang

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 2, page 387-401
  • ISSN: 0011-4642

Abstract

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We construct some nondecreasing quantities associated to the first eigenvalue of - Δ φ + c R ( c ≥ 1 2 ( n - 2 ) / ( n - 1 ) ) along the Yamabe flow, where Δ φ is the Witten-Laplacian operator with a C 2 function φ . We also prove a monotonic result on the first eigenvalue of - Δ φ + 1 4 ( n / ( n - 1 ) ) R along the Yamabe flow. Moreover, we establish some nondecreasing quantities for the first eigenvalue of - Δ φ + c R a with a ∈ ( 0 , 1 ) along the Yamabe flow.

How to cite

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Zhang, Liangdi. "Monotonicity of first eigenvalues along the Yamabe flow." Czechoslovak Mathematical Journal 71.2 (2021): 387-401. <http://eudml.org/doc/297520>.

@article{Zhang2021,
abstract = {We construct some nondecreasing quantities associated to the first eigenvalue of $-\Delta _\phi +cR$$(c\ge \frac\{1\}\{2\}(n-2)/(n-1))$ along the Yamabe flow, where $\Delta _\phi $ is the Witten-Laplacian operator with a $C^2$ function $\phi $. We also prove a monotonic result on the first eigenvalue of $-\Delta _\phi + \frac\{1\}\{4\} (n/ (n-1))R$ along the Yamabe flow. Moreover, we establish some nondecreasing quantities for the first eigenvalue of $-\Delta _\phi +cR^a$ with $a\in (0,1)$ along the Yamabe flow.},
author = {Zhang, Liangdi},
journal = {Czechoslovak Mathematical Journal},
keywords = {monotonicity; first eigenvalue; Witten-Laplacian operator; Yamabe flow},
language = {eng},
number = {2},
pages = {387-401},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Monotonicity of first eigenvalues along the Yamabe flow},
url = {http://eudml.org/doc/297520},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Zhang, Liangdi
TI - Monotonicity of first eigenvalues along the Yamabe flow
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 387
EP - 401
AB - We construct some nondecreasing quantities associated to the first eigenvalue of $-\Delta _\phi +cR$$(c\ge \frac{1}{2}(n-2)/(n-1))$ along the Yamabe flow, where $\Delta _\phi $ is the Witten-Laplacian operator with a $C^2$ function $\phi $. We also prove a monotonic result on the first eigenvalue of $-\Delta _\phi + \frac{1}{4} (n/ (n-1))R$ along the Yamabe flow. Moreover, we establish some nondecreasing quantities for the first eigenvalue of $-\Delta _\phi +cR^a$ with $a\in (0,1)$ along the Yamabe flow.
LA - eng
KW - monotonicity; first eigenvalue; Witten-Laplacian operator; Yamabe flow
UR - http://eudml.org/doc/297520
ER -

References

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