Zobrazeno 1 - 10
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pro vyhledávání: '"Shoo Seto"'
Autor:
Shoo Seto
We survey results on the first (nontrivial) eigenvalue of the p p -Laplace operator for both the Dirichlet and Neumann/closed condition on Riemannian manifolds. We also discuss an extension of the p p -Laplace operator to act on differential forms. S
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b71817adbab68261aa367aeab333d1f0
Publikováno v:
Mathematische Zeitschrift. 296:595-613
We prove a sharp Zhong–Yang type eigenvalue lower bound for closed Riemannian manifolds with control on integral Ricci curvature.
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https://explore.openaire.eu/search/publication?articleId=doi_________::04d8fdf0bda6ef33f5c0eed3e72a785d
https://doi.org/10.1007/s00209-019-02448-w
https://doi.org/10.1007/s00209-019-02448-w
Autor:
Casey Blacker, Shoo Seto
Publikováno v:
Proceedings of the American Mathematical Society. 147:2197-2206
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5e06fa2ebc13a44c9492e817ea30389f
https://doi.org/10.1090/proc/14395
https://doi.org/10.1090/proc/14395
Autor:
Guofang Wei, Shoo Seto
Publikováno v:
Nonlinear Analysis. 163:60-70
We give various estimates of the first eigenvalue of the p -Laplace operator on closed Riemannian manifold with integral curvature conditions.
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https://explore.openaire.eu/search/publication?articleId=doi_________::2c121a2e345192adc2ab882c7cb7eac6
https://doi.org/10.1016/j.na.2017.07.007
https://doi.org/10.1016/j.na.2017.07.007
We compute Dirichlet eigenvalues and eigenfunctions explicitly for spherical lunes and the spherical triangles which are half the lunes, and show that the fundamental gap goes to infinity when the angle of the lune goes to zero. Then we show the sphe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7d4ec7e4296f8771db05761b2b6c0056
Publikováno v:
J. Differential Geom. 112, no. 2 (2019), 347-389
In their celebrated work, B. Andrews and J. Clutterbuck proved the fundamental gap (the difference between the first two eigenvalues) conjecture for convex domains in the Euclidean space and conjectured similar results holds for spaces with constant
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::68918554341ab421a2f8877417fc9e52
https://doi.org/10.4310/jdg/1559786428
https://doi.org/10.4310/jdg/1559786428
Autor:
Shoo Seto
we introduce a generalization of the $p$-Laplace operator to act on differential forms and generalize an estimate of Gallot-Meyer for the first nonzero eigenvalue on closed Riemannian manifolds.
comments welcome
comments welcome
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ba457ce589162df29012b939d9983aeb
http://arxiv.org/abs/1903.05840
http://arxiv.org/abs/1903.05840
Autor:
Shoo Seto
Publikováno v:
Contemporary Mathematics. :179-184
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::26f509287119dde88ebc6901461ceb0c
https://doi.org/10.1090/conm/681/13684
https://doi.org/10.1090/conm/681/13684
In [SWW16, HW17] it is shown that the difference of the first two eigenvalues of the Laplacian with Dirichlet boundary condition on convex domain with diameter $D$ of sphere $\mathbb S^n$ is $\geq 3 \frac{\pi^2}{D^2}$ when $n \geq 3$. We prove the sa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::49b4c834264adf3e71d403da4772d21a
http://arxiv.org/abs/1803.01115
http://arxiv.org/abs/1803.01115
Publikováno v:
The Journal of Geometric Analysis. 26:2602-2638
We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated with the kth tensor powers of a positive line bundle L in a \(\frac{1}{\sqrt{k}}\)-neighborhood of the diagonal using elementary methods. We use
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a603fa9ad673e4bfe2b27f6f264f6eff
https://doi.org/10.1007/s12220-015-9641-3
https://doi.org/10.1007/s12220-015-9641-3