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In this paper we study monotonicity the first eigenvalue for a class of $(p,q)$-Laplace operator acting on the space of functions on a closed Riemannian manifold. We find the first variation formula for the first eigenvalue of a class of $(p,q)$-Laplacians on a closed Riemannian manifold evolving by the Ricci-Bourguignon flow and show that the first eigenvalue on a closed Riemannian manifold along the Ricci-Bourguignon flow is increasing provided some conditions. At the end of paper, we find some applications in $2$-dimensional and $3$-dimensional manifolds.
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참고문헌 (24)
참고문헌 신청
H. Amann / 1972 / Lusternik-Schnirelman theory and non-linear eigenvalue problems / Math. Ann 199:55~72
Shahroud Azami / 2018 / The rst eigenvalue of some (p; g)-Laplacian and geometric estimates / 대한수학회논문집 33(1):317~323
L. Boccardo / 2002 / Some remarks on a system of quasilinear elliptic equations / NoDEA Nonlinear Dierential Equations Appl 9(3):309~323
J.-P. Bourguignon / 1981 / Ricci curvature and Einstein metrics, in Global dierential geometry and global analysis (Berlin, 1979), 42-63 / Lecture Notes in Math 838
X. Cao / 2007 / Eigenvalues of (−∆ + R2) on manifolds with nonnegative curvature operator / Math. Ann 337(2):435~441
Shahroud Azami / 2018 / The rst eigenvalue of some (p; g)-Laplacian and geometric estimates / 대한수학회논문집 33(1):317~323
L. Boccardo / 2002 / Some remarks on a system of quasilinear elliptic equations / NoDEA Nonlinear Dierential Equations Appl 9(3):309~323
J.-P. Bourguignon / 1981 / Ricci curvature and Einstein metrics, in Global dierential geometry and global analysis (Berlin, 1979), 42-63 / Lecture Notes in Math 838
X. Cao / 2007 / Eigenvalues of (−∆ + R2) on manifolds with nonnegative curvature operator / Math. Ann 337(2):435~441
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