The sharp isoperimetric inequality for varifolds in codimension two

@misc{tsiamis2026sharp,
  title = {{The sharp isoperimetric inequality for varifolds in codimension two}},
  author = {Raphael Tsiamis},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22447},
  eprint = {2609.22447},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22447},
}

TY  - UNPB
TI  - The sharp isoperimetric inequality for varifolds in codimension two
AU  - Raphael Tsiamis
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.22447
UR  - https://arxiv.org/abs/2609.22447
AB  - We prove a Michael-Simon inequality for a class of varifolds in Euclidean space that includes all integral varifolds with locally bounded first variation of arbitrary dimension and codimension. In codimension $2$, this inequality is sharp and implies the sharp isoperimetric inequality for varifolds, which attains equality precisely for the round disk. Our proof uses the optimal transportation approach of Brendle-Eichmair.
ER  -