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Anomaly Flow II: Estimates and Long-time Existence for the Coupled Flow
Abstract
In this follow-up to \cite{Sua25}, we extend the results to the coupled anomaly flow which incorporates the evolution of a Hermitian metric on a holomorphic vector bundle over a compact complex $3$-fold with general slope parameter α'. This yields a similar sufficient smallness condition on the slope parameter α' in order to extend the flow on $[0, τ)$ to [0, τ+ ε). We also augment the argument of \cite{Sua25} slightly to fix the peculiarity of the units in the condition for α' for the k = 1 case.
Related
- Long-time existence and uniqueness of the heterotic G2 flow
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- On the existence of coupled extremal Kähler metrics on ruled surfaces
BibTeX
@misc{suan2026anomaly,
title = {{Anomaly Flow II: Estimates and Long-time Existence for the Coupled Flow}},
author = {Caleb Suan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15009},
eprint = {2610.15009},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15009},
}
RIS
TY - UNPB
TI - Anomaly Flow II: Estimates and Long-time Existence for the Coupled Flow
AU - Caleb Suan
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15009
UR - https://arxiv.org/abs/2610.15009
AB - In this follow-up to \cite{Sua25}, we extend the results to the coupled anomaly flow which incorporates the evolution of a Hermitian metric on a holomorphic vector bundle over a compact complex $3$-fold with general slope parameter α'. This yields a similar sufficient smallness condition on the slope parameter α' in order to extend the flow on $[0, τ)$ to [0, τ+ ε). We also augment the argument of \cite{Sua25} slightly to fix the peculiarity of the units in the condition for α' for the k = 1 case.
ER -