Remarks on Bernstein theorems for translating solitons
Li Ma
TL;DR
This paper investigates properties of translating solitons in Euclidean space, providing conditions for Bernstein theorems and offering a simplified proof outline for existing results.
Contribution
It introduces a new condition for Bernstein theorems for translating solitons and simplifies the proof of a classical Bernstein theorem.
Findings
Derived a condition for Bernstein theorems in translating solitons
Analyzed volume growth of intersections with Euclidean balls
Provided a simplified proof outline for Bernstein theorem
Abstract
In this paper, we study the properties of potential function of the translating soliton in and the volume growth of the intersection of Euclidean balls with . We give a condition to obtain the Bernstein theorem for the translating solitons. We also give an outline of a simple proof of the Bernstein theorem due to Bombieri-De Giorgi-Miranda.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Point processes and geometric inequalities