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Volumn 3, Issue 2, 1999, Pages 235-242

General formulae for the lower bound of the first two Dirichlet eigenvalues

Author keywords

Dirichlet eigenvalue; Riemannian manifold

Indexed keywords


EID: 0040219799     PISSN: 10275487     EISSN: None     Source Type: Journal    
DOI: 10.11650/twjm/1500407095     Document Type: Article
Times cited : (4)

References (11)
  • 1
    • 49549132663 scopus 로고
    • On extension of the Brunn-Minkowski and Prekojia-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
    • H. K. Brascamp and E. H. Lieb, On extension of the Brunn-Minkowski and Prekojia-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, J. Funct. Anal. 22 (1976), 366-389.
    • (1976) J. Funct. Anal. , vol.22 , pp. 366-389
    • Brascamp, H.K.1    Lieb, E.H.2
  • 3
    • 84972500359 scopus 로고
    • The splitting theorem for manifolds of non-negative Ricci curvature
    • J. Cheeger and D. Gromoll, The splitting theorem for manifolds of non-negative Ricci curvature, J. Differential Geom. 6 (1971), 119-128.
    • (1971) J. Differential Geom. , vol.6 , pp. 119-128
    • Cheeger, J.1    Gromoll, D.2
  • 4
    • 0346477732 scopus 로고    scopus 로고
    • General formula for lower bound of the first eigenvalue on riemannian manifolds
    • M. F. Chen and F. Y. Wang, General formula for lower bound of the first eigenvalue on Riemannian manifolds, Sci. China Ser. A 40 (1997), 384-394.
    • (1997) Sci. China Ser. A , vol.40 , pp. 384-394
    • Chen, M.F.1    Wang, F.Y.2
  • 5
    • 21744453864 scopus 로고    scopus 로고
    • Estimation of spectral gap for elliptic operators
    • M. F. Chen and F. Y. Wang, Estimation of spectral gap for elliptic operators, Trans. Amer. Math. Soc. 349 (1997), 1209-1237.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 1209-1237
    • Chen, M.F.1    Wang, F.Y.2
  • 6
    • 51249169755 scopus 로고
    • Spectrum, harmonic functions, and hyperbolic metric spaces
    • Y. Kifer, Spectrum, harmonic functions, and hyperbolic metric spaces, Israel J. Math. 89 (1995), 377-428.
    • (1995) Israel J. Math. , vol.89 , pp. 377-428
    • Kifer, Y.1
  • 8
    • 84972517072 scopus 로고
    • An upper bound to the spectrum of Δ on a manifold of negative curvature
    • H. P. McKean, An upper bound to the spectrum of Δ on a manifold of negative curvature, J. Differential Geom. 4 (1970), 359-366.
    • (1970) J. Differential Geom. , vol.4 , pp. 359-366
    • McKean, H.P.1
  • 9
    • 21844523092 scopus 로고
    • Estimates of the first Dirichlet eigenvalue by using diffusion processes
    • F. Y. Wang, Estimates of the first Dirichlet eigenvalue by using diffusion processes, Probab. Theory Related Fields 101 (1995), 363-369.
    • (1995) Probab. Theory Related Fields , vol.101 , pp. 363-369
    • Wang, F.Y.1
  • 10
    • 0038842922 scopus 로고    scopus 로고
    • Estimates of the gap between the first two Dirichlet eigenvalues
    • to appear
    • F. Y. Wang, Estimates of the gap between the first two Dirichlet eigenvalues, to appear in J. London Math. Soc..
    • J. London Math. Soc.
    • Wang, F.Y.1
  • 11
    • 0001108250 scopus 로고
    • Lower bounds of the gap between the first and second eigenvalues of the Schrödinger operator
    • Q. H. Yu and J. Q. Zhong, Lower bounds of the gap between the first and second eigenvalues of the Schrödinger operator, Trans. Amer. Math. Soc. 294 (1986), 341-349.
    • (1986) Trans. Amer. Math. Soc. , vol.294 , pp. 341-349
    • Yu, Q.H.1    Zhong, J.Q.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.