Sharp $C^{1,\bar1}$ estimates in Kähler quantization and non-pluripolar Radon measures
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908808107786240 |
|---|---|
| author | Błocki, Zbigniew Darvas, Tamás |
| author_facet | Błocki, Zbigniew Darvas, Tamás |
| contents | Let $K_φ$ denote the weighted Bergman kernel associated to a plurisubharmonic function $φ$. We obtain upper bounds and positive lower bounds for the Bergman metric $i\partial \bar{\partial} \log K_φ$, expressed solely in terms of upper bounds and positive lower bounds of $i\partial \bar{\partial}φ$. Our approach applies in both local and compact Kähler settings. As an immediate application we obtain the optimal $C^{1,α}$-convergence for the quantization of Kähler currents with bounded coefficients. We also show that any non-pluripolar Radon measure on a compact Kähler manifold admits a quantization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03111 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp $C^{1,\bar1}$ estimates in Kähler quantization and non-pluripolar Radon measures Błocki, Zbigniew Darvas, Tamás Differential Geometry Mathematical Physics Complex Variables Let $K_φ$ denote the weighted Bergman kernel associated to a plurisubharmonic function $φ$. We obtain upper bounds and positive lower bounds for the Bergman metric $i\partial \bar{\partial} \log K_φ$, expressed solely in terms of upper bounds and positive lower bounds of $i\partial \bar{\partial}φ$. Our approach applies in both local and compact Kähler settings. As an immediate application we obtain the optimal $C^{1,α}$-convergence for the quantization of Kähler currents with bounded coefficients. We also show that any non-pluripolar Radon measure on a compact Kähler manifold admits a quantization. |
| title | Sharp $C^{1,\bar1}$ estimates in Kähler quantization and non-pluripolar Radon measures |
| topic | Differential Geometry Mathematical Physics Complex Variables |
| url | https://arxiv.org/abs/2602.03111 |