4 citations · 5 across the 5 of their papers we have counts for
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Convergence of Laplacian Eigenmaps and its Rate for Submanifolds with Singularities
Masayuki Aino
In this paper, we give a spectral approximation result for the Laplacian on submanifolds of Euclidean spaces with singularities by the -neighborhood graph constructed from rando…
Convergence to the Product of the Standard Spheres and Eigenvalues of the Laplacian
Masayuki Aino
We show a Gromov-Hausdorff approximation to the product of the standard spheres for Riemannian manifolds with positive Ricci curvature under some pinching condi…
Lichnerowicz-Obata Estimate, Almost Parallel -form and Almost Product Manifolds
Masayuki Aino
We show a Lichnerowicz-Obata type estimate for the first eigenvalue of the Laplacian of -dimensional closed Riemannian manifolds with an almost parallel -form ($2\leq p \leq…
Sphere theorems and eigenvalue pinching without positive Ricci curvature assumption
Masayuki Aino
Considering the almost rigidity of the Obata theorem, we generalize Petersen and Aubry's sphere theorem about eigenvalue pinching without assuming the positivity of Ricci curvature…
Riemannian Invariants that Characterize Rotational Symmetries of the Standard Sphere
Masayuki Aino
Inspired by the Lichnerowicz-Obata theorem for the first eigenvalue of the Laplacian, we define a new family of invariants for closed Riemannian manifolds. The value o…