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PreprintarXiv licencearXiv

A symmetric counterexample to Strang's conjecture for bivariate C1 cubic splines on triangulations

  • Pratyush Potu
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Abstract

We exhibit a triangulation of an equilateral triangle for which the space of bivariate C1 cubic splines has dimension larger than the dimension formula conjectured by Strang. Notably, the triangulation is such that no two edges sharing a vertex are collinear, and the triangulation is invariant under the action of the isometry group (D3) of the equilateral triangle which is triangulated.

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Cite

BibTeXRIS
BibTeX
@misc{potu2026symmetric,
  title = {{A symmetric counterexample to Strang's conjecture for bivariate $C^1$ cubic splines on triangulations}},
  author = {Pratyush Potu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08470},
  eprint = {2610.08470},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08470},
}
RIS
TY  - UNPB
TI  - A symmetric counterexample to Strang's conjecture for bivariate C^1 cubic splines on triangulations
AU  - Pratyush Potu
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08470
UR  - https://arxiv.org/abs/2610.08470
AB  - We exhibit a triangulation of an equilateral triangle for which the space of bivariate C^1 cubic splines has dimension larger than the dimension formula conjectured by Strang. Notably, the triangulation is such that no two edges sharing a vertex are collinear, and the triangulation is invariant under the action of the isometry group (D_3) of the equilateral triangle which is triangulated.
ER  -