Pith. sign in

REVIEW 2 cited by

Classification of bubble-sheet ovals in $\mathbb{R}^{4}$

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2209.04931 v3 pith:MI3ZUFO5 submitted 2022-09-11 math.DG math.AP

Beomjun Choi , Panagiota Daskalopoulos , Wenkui Du , Robert Haslhofer , Natasa Sesum This is my paper · ORCID
classification math.DGmath.AP
keywords mathbbtextrmancientauthorbubble-sheetclassificationconstructedfourth
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

In this paper, we prove that any bubble-sheet oval for the mean curvature flow in $\mathbb{R}^4$, up to scaling and rigid motion, either is the $\textrm{O}(2)\times \textrm{O}(2)$-symmetric ancient oval constructed by Hershkovits and the fourth author, or belongs to the one-parameter family of $\mathbb{Z}_2^2\times \textrm{O}(2)$-symmetric ancient ovals constructed by the third and fourth author. In particular, this seems to be the first instance of a classification result for geometric flows that are neither cohomogeneity-one nor selfsimilar.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Type-I Blowup Solutions for Yang-Mills Flow

    math.DG 2024-11 conditional novelty 8.0 of 10

    For 5 to 9 dimensions, an infinite-dimensional family of Yang-Mills flow solutions is constructed that converge, modulo gauge, to the homothetically shrinking soliton W, including asymmetric Type-I blowups.

  2. Passing through nondegenerate singularities in mean curvature flows

    math.DG 2025-01 conditional novelty 7.0 of 10

    Mean curvature flows through nondegenerate cylindrical singularities undergo an isolated, graphical surgery event whose topology change equals an (n-k)-surgery, matching Morse level sets.

Pith tools