Classification of semigraphical translators
Abstract We complete the classification of semigraphical translators for mean curvature flow in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>𝐑</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> {\mathbf{R}^{3}} that was initiated by Hoffman, Martín and White. Specifically, we show that there is no solution to the translator equation on the upper half-plane with alternating positive and negative infinite boundary values, and we prove the uniqueness of pitchfork and helicoid translators. The proofs use Morse–Radó theory for translators and an angular maximum principle.
Authors
- Mariel Sáez (ORCID: https://orcid.org/0000-0002-3787-9990)
- Brian White (ORCID: https://orcid.org/0000-0002-0339-7600)
- Francisco Martín (ORCID: https://orcid.org/0000-0001-8380-0465)
- Raphael Tsiamis (ORCID: https://orcid.org/0009-0006-6113-467X)
Institutions
- Pontificia Universidad Católica de Chile (CL)
- Universidad de Granada (ES)
- Columbia University (US)
- Stanford University (US)
Publication Details
- Journal
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- Published
- 2026-06-25
- DOI
- https://doi.org/10.1515/crelle-2026-0052
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Agencia Estatal de Investigación