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PreprintCC BY-NC-SA 4.0arXiv

Korevaar-Schoen Energy and Interpolations of Fractional Sobolev mappings on Carnot groups

  • Yihan Cui
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Abstract

This paper investigates the theory of fractional Sobolev mappings between Carnot groups, with a particular focus on the Korevaar-Schoen energy functional and interpolation properties. We establish that weak contact equations hold for fractional Sobolev mappings on Carnot groups, generalizing classical results from the Euclidean setting to the sub-Riemannian framework. Our main results include: (1) the proof that fractional Sobolev mappings satisfying weak contact equations belong to the horizontal fractional Sobolev space WHs−λ,q(Ω;G2) for any sufficiently small λ>0; (2) interpolation theorems for fractional Sobolev mappings between Carnot groups, demonstrating that the limiting behavior as s → 1 recovers the first-order Sobolev space; (3) a rigorous treatment of the Korevaar-Schoen energy on Carnot groups, including a characterization of its minimizers via horizontal differential forms.

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Cite

BibTeXRIS
BibTeX
@misc{cui2026korevaarschoen,
  title = {{Korevaar-Schoen Energy and Interpolations of Fractional Sobolev mappings on Carnot groups}},
  author = {Yihan Cui},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10551},
  eprint = {2610.10551},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10551},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Korevaar-Schoen Energy and Interpolations of Fractional Sobolev mappings on Carnot groups
AU  - Yihan Cui
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.10551
UR  - https://arxiv.org/abs/2610.10551
AB  - This paper investigates the theory of fractional Sobolev mappings between Carnot groups, with a particular focus on the Korevaar-Schoen energy functional and interpolation properties. We establish that weak contact equations hold for fractional Sobolev mappings on Carnot groups, generalizing classical results from the Euclidean setting to the sub-Riemannian framework. Our main results include: (1) the proof that fractional Sobolev mappings satisfying weak contact equations belong to the horizontal fractional Sobolev space W_H^s−λ,q(Ω;G_2) for any sufficiently small λ>0; (2) interpolation theorems for fractional Sobolev mappings between Carnot groups, demonstrating that the limiting behavior as s → 1 recovers the first-order Sobolev space; (3) a rigorous treatment of the Korevaar-Schoen energy on Carnot groups, including a characterization of its minimizers via horizontal differential forms.
ER  -