On Weighted Twisted K-Energy and Its Applications
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912959067848704 |
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| author | Xiao, Xia |
| author_facet | Xiao, Xia |
| contents | We establish the convexity of the weighted twisted Mabuchi K-energy functional along geodesics in the finite energy space $\mathcal{E}^{1,T}(X,ω)$, covering the case of divisors with mixed cusp and conic singularities. We then prove that coercivity (relative to the complex torus) of this functional is an open condition under cone angle perturbations. This is obtained from a general result of independent interest, which shows the stability of the coercivity under perturbations by certain twist currents. In particular, this yields the openness for the existence for cscK cone metrics and proves that coercivity at the cusp limit implies existence of cscK cone metrics for small cone angles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20302 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Weighted Twisted K-Energy and Its Applications Xiao, Xia Differential Geometry 32Q20, 32U05, 53C55, 32U15 We establish the convexity of the weighted twisted Mabuchi K-energy functional along geodesics in the finite energy space $\mathcal{E}^{1,T}(X,ω)$, covering the case of divisors with mixed cusp and conic singularities. We then prove that coercivity (relative to the complex torus) of this functional is an open condition under cone angle perturbations. This is obtained from a general result of independent interest, which shows the stability of the coercivity under perturbations by certain twist currents. In particular, this yields the openness for the existence for cscK cone metrics and proves that coercivity at the cusp limit implies existence of cscK cone metrics for small cone angles. |
| title | On Weighted Twisted K-Energy and Its Applications |
| topic | Differential Geometry 32Q20, 32U05, 53C55, 32U15 |
| url | https://arxiv.org/abs/2602.20302 |