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Metric entropy of Kähler potentials
Abstract
We prove sharp metric entropy estimates for spaces of Kähler potentials. In complex dimension n, normalized potentials have Kolmogorov entropy of order e−n in the background L1 metric. On a polarized manifold, a relative-entropy sublevel has the same order in the Mabuchi--Darvas d1 metric, including its full finite-energy closure. The upper bound is CX(1+B)n+1e−n for entropy budget B. For toric potentials, the sharp exponent is n/2.
Related
- Kähler-Finsler rigidity of the Kobayashi metric and the Kähler base of weakly Kähler-Finsler metrics
- Canonical Bochner-Kähler potentials via the Sasaki-Kähler correspondence
- Spectral Estimates for Compact Riemann Surfaces via Kähler Potentials
- Spatial degeneracy along weak geodesics in the space of Kähler potentials
- A complete Kähler metric on ℂn of nonnegative Ricci curvature with Euclidean volume growth and nonunique asymptotic cone
BibTeX
@misc{hisamoto2026metric,
title = {{Metric entropy of Kähler potentials}},
author = {Tomoyuki Hisamoto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29002},
eprint = {2609.29002},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29002},
}
RIS
TY - UNPB
TI - Metric entropy of Kähler potentials
AU - Tomoyuki Hisamoto
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29002
UR - https://arxiv.org/abs/2609.29002
AB - We prove sharp metric entropy estimates for spaces of Kähler potentials. In complex dimension n, normalized potentials have Kolmogorov entropy of order e^−n in the background L^1 metric. On a polarized manifold, a relative-entropy sublevel has the same order in the Mabuchi--Darvas d_1 metric, including its full finite-energy closure. The upper bound is C_X(1+B)^n+1e^−n for entropy budget B. For toric potentials, the sharp exponent is n/2.
ER -