3 papers
math.DG2025
Calibrated submanifolds with flat normal bundles
W. Jacob Ogden
We show that submanifolds of Euclidean space which are calibrated by a constant-coefficient differential form and have flat normal bundles are planes. In fact, in a Riemannian mani…
math.DG2024
Grim Raindrop: A Translating Solution to Curve Diffusion Flow
W. Jacob Ogden, Micah Warren
We show the existence of a properly immersed translating solution to curve diffusion flow in the plane. Curve diffusion flow is a higher order version of curve shortening flow, nam…
math.AP2023
Remarks on the Complex Euler Equations
Dallas Albritton, W. Jacob Ogden
We consider a complexification of the Euler equations introduced by Šverák which conserves energy. We prove that these complex Euler equations are nonlinearly ill-posed below analy…