# Scherk-like Translators for Mean Curvature Flow

## TL;DR

This paper constructs and analyzes a new family of solutions called translators for mean curvature flow, including novel examples with potential applications to understanding singularities in surface evolution.

## Contribution

It proves existence and uniqueness of a two-parameter family of translators and introduces new examples, some resembling minimal surfaces and others with no minimal analogs.

## Key findings

- Existence and uniqueness of a two-parameter family of translators.
- Introduction of new translator examples with diverse geometric properties.
- Potential relevance of certain examples as blowups at singularities in mean curvature flow.

## Abstract

We prove existence and uniqueness for a two-parameter family of translators for mean curvature flow. We get additional examples by taking limits at the boundary of the parameter space. Some of the translators resemble well-known minimal surfaces (Scherk's doubly periodic minimal surfaces, helicoids), but others have no minimal surface analogs. A one-parameter subfamily of the examples (the pitchforks) have finite topology and quadratic area growth, and thus might arise as blowups at singularities of initially smooth, closed surfaces flowing by mean curvature flow.