TY - JOUR
T1 - Estimates of eigenvalues of the Laplacian by a reduced number of subsets
AU - Funano, Kei
N1 - Publisher Copyright:
© 2017, Hebrew University of Jerusalem.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - Chung–Grigor’yan–Yau’s inequality describes upper bounds of eigenvalues of the 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 Alexandrov spaces satisfying CD(0,∞). We will also discuss a related conjecture for some universal inequality among eigenvalues of the Laplacian.
AB - Chung–Grigor’yan–Yau’s inequality describes upper bounds of eigenvalues of the 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 Alexandrov spaces satisfying CD(0,∞). We will also discuss a related conjecture for some universal inequality among eigenvalues of the Laplacian.
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U2 - 10.1007/s11856-017-1453-7
DO - 10.1007/s11856-017-1453-7
M3 - Article
AN - SCOPUS:85015794755
VL - 217
SP - 413
EP - 433
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
SN - 0021-2172
IS - 1
ER -