PreprintarXiv licencearXiv
Gradient nature of Laplacian growth
Abstract
For a class of growth processes of Laplacian type in the plane, we suggest an interpretation as a ``gradient descent'' in the space of smooth closed curves. More precisely, we show that boundary of a growing domain moves along a gradient of a certain functional in the space of curves. In the simplest cases this functional is log (1/r), where r is the external conformal radius of the growing domain.
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BibTeX
@misc{zabrodin2026gradient,
title = {{Gradient nature of Laplacian growth}},
author = {A. Zabrodin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21430},
eprint = {2609.21430},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21430},
}
RIS
TY - UNPB
TI - Gradient nature of Laplacian growth
AU - A. Zabrodin
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21430
UR - https://arxiv.org/abs/2609.21430
AB - For a class of growth processes of Laplacian type in the plane, we suggest an interpretation as a ``gradient descent'' in the space of smooth closed curves. More precisely, we show that boundary of a growing domain moves along a gradient of a certain functional in the space of curves. In the simplest cases this functional is log (1/r), where r is the external conformal radius of the growing domain.
ER -