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arXiv · 2503.21523

A weak energy identity for $(n+\alpha)$-harmonic maps with a free boundary in a sphere

Dorian Martino·Katarzyna Mazowiecka·Rémy Rodiac
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Abstract

In this article, we show that sequences of $(n+\alpha)$-harmonic maps with a free boundary in $\mathbb S^{d-1}$, where $\alpha$ is a parameter tending to zero, converge to a bubble tree. For such sequences, we prove in detail that the limiting energy is equal to the energy of the macroscopic limit plus the sum of the energies of certain ``bubbles'', each multiplied by a corresponding coefficient.

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Dorian Martino, Katarzyna Mazowiecka, Rémy Rodiac. 2025-03-27. A weak energy identity for $(n+\alpha)$-harmonic maps with a free boundary in a sphere. https://arxiv.org/abs/2503.21523

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