Zobrazeno 1 - 10
of 64
pro vyhledávání: '"Funano, Kei"'
Autor:
Cavallina, Lorenzo, Funano, Kei, Henrot, Antoine, Lemenant, Antoine, Lucardesi, Ilaria, Sakaguchi, Shigeru
Neumann eigenvalues being non-decreasing with respect to domain inclusion, it makes sense to study the two shape optimization problems $\min\{\mu_k(\Omega):\Omega \mbox{ convex},\Omega \subset D, \}$ (for a given box $D$) and $\max\{\mu_k(\Omega):\Om
Externí odkaz:
http://arxiv.org/abs/2312.13747
Autor:
Funano, Kei
In this short survey, we derive some weyl-type universal inequalities of eigenvalues of the Laplacian on a closed Riemannian manifold of nonnegative Ricci curvature. We also give upper bounds for the $L_{\infty}$ norm of eigenfunctions of the Laplaci
Externí odkaz:
http://arxiv.org/abs/2310.02938
Autor:
Funano, Kei
We obtain a new upper bound for Neumann eigenvalues of the Laplacian on a bounded convex domain in Euclidean space. As an application of the upper bound we derive universal inequalities for Neumann eigenvalues of the Laplacian.
Comment: Final ve
Comment: Final ve
Externí odkaz:
http://arxiv.org/abs/2305.04398
Autor:
Funano, Kei
Given a convex domain and its convex sub-domain we prove a variant of domain monotonicity for the Neumann eigenvalues of the Laplacian. As an application of our method we also obtain an upper bound for Neumann eigenvalues of the Laplacian of a convex
Externí odkaz:
http://arxiv.org/abs/2202.03598
Autor:
Funano, Kei, Sakurai, Yohei
We introduce higher-order Poincar'e constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of the weighted Laplacian and the first nontrivial eigenvalue of the $p$
Externí odkaz:
http://arxiv.org/abs/1907.03617
Autor:
Funano, Kei, Sakurai, Yohei
We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponentially. Applying the method of Colding a
Externí odkaz:
http://arxiv.org/abs/1712.09084
Autor:
Alpert, Hannah, Funano, Kei
In this paper we prove the following. Let $\Sigma$ be an $n$--dimensional closed hyperbolic manifold and let $g$ be a Riemannian metric on $\Sigma \times \mathbb{S}^1$. Given an upper bound on the volumes of unit balls in the Riemannian universal cov
Externí odkaz:
http://arxiv.org/abs/1705.02923
Autor:
Funano, Kei
We apply Gromov's ham sandwich method to get (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Lap
Externí odkaz:
http://arxiv.org/abs/1609.05549
Autor:
Funano, Kei
Chung-Grigor'yan-Yau's inequality describes upper bounds of eigenvalues of Laplacian in terms of subsets ("input") and their volumes. In this paper we will show that we can reduce "input" in Chung-Grigor'yan-Yau's inequality in the setting of Alexand
Externí odkaz:
http://arxiv.org/abs/1601.07581
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