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PreprintCC BY 4.0arXiv

Topping's conjecture for solutions of harmonic map flow with isolated bubbles

  • Melanie Rupflin
  • Alex Waldron
  • Sebastian Woodward
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Abstract

By establishing a weighted Lojasiewicz-Simon inequality for maps which are close to a fixed harmonic map modulo scaling, we prove Topping's conjecture on continuity of the body map in the case of finite time singularities at which only isolated bubbles form.

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Cite

BibTeXRIS
BibTeX
@misc{rupflin2026toppings,
  title = {{Topping's conjecture for solutions of harmonic map flow with isolated bubbles}},
  author = {Melanie Rupflin and Alex Waldron and Sebastian Woodward},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13746},
  eprint = {2610.13746},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13746},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Topping's conjecture for solutions of harmonic map flow with isolated bubbles
AU  - Melanie Rupflin
AU  - Alex Waldron
AU  - Sebastian Woodward
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13746
UR  - https://arxiv.org/abs/2610.13746
AB  - By establishing a weighted Lojasiewicz-Simon inequality for maps which are close to a fixed harmonic map modulo scaling, we prove Topping's conjecture on continuity of the body map in the case of finite time singularities at which only isolated bubbles form.
ER  -