Volume 4, Issue 4
An Eigenvalue Problem on Negatively Curved Manifolds
DOI:

J. Part. Diff. Eq.,4(1991),pp.1-8

Published online: 1991-04

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• Abstract

Consider the eigenvalue problem: Δgu - λKu = 0 \quad in D where D is the unit disc of the complex plane, g is a complete metric conformal to the Poincaré metric on D, and K is the Gaussian curvature. It is shown that if λ > \frac{1}{2} (λ > \frac{1}{4}in the case of K ≤ 0), then the above problem has no positive solutions.

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Eigenvalue problem complete manifolds negative curvature

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@Article{JPDE-4-1, author = {Fang Hua Lin}, title = {An Eigenvalue Problem on Negatively Curved Manifolds}, journal = {Journal of Partial Differential Equations}, year = {1991}, volume = {4}, number = {4}, pages = {1--8}, abstract = { Consider the eigenvalue problem: Δgu - λKu = 0 \quad in D where D is the unit disc of the complex plane, g is a complete metric conformal to the Poincaré metric on D, and K is the Gaussian curvature. It is shown that if λ > \frac{1}{2} (λ > \frac{1}{4}in the case of K ≤ 0), then the above problem has no positive solutions.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5779.html} }
TY - JOUR T1 - An Eigenvalue Problem on Negatively Curved Manifolds AU - Fang Hua Lin JO - Journal of Partial Differential Equations VL - 4 SP - 1 EP - 8 PY - 1991 DA - 1991/04 SN - 4 DO - http://dor.org/ UR - https://global-sci.org/intro/jpde/5779.html KW - Eigenvalue problem KW - complete manifolds KW - negative curvature AB - Consider the eigenvalue problem: Δgu - λKu = 0 \quad in D where D is the unit disc of the complex plane, g is a complete metric conformal to the Poincaré metric on D, and K is the Gaussian curvature. It is shown that if λ > \frac{1}{2} (λ > \frac{1}{4}in the case of K ≤ 0), then the above problem has no positive solutions.
Fang Hua Lin. (1970). An Eigenvalue Problem on Negatively Curved Manifolds. Journal of Partial Differential Equations. 4 (4). 1-8. doi:
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