11 papers
Elastic Curves via Geometric Mechanics
Oliver Gross, Rohit Jammula, Albert Chern
Elastic curves are the mathematical shapes of thin elastic rods in equilibrium, with deep connections to mechanics, geometry, and computer graphics. Traditionally described as stat…
Neural Representation of Minimal Surfaces
Jiayin Sun, Albert Chern
We propose a neural representation for minimal surfaces. Unlike prior approaches based on discretization or Physics-Informed Neural Networks (PINNs), where meshes or neural fields…
Vakonomic Fluids
Ritoban Roy-Chowdhury, Mohammad Sina Nabizadeh, Oliver Gross +2
We introduce a novel discretization of the incompressible Euler equations based on their interpretation as geodesic equations on the Lie group of volume-preserving diffeomorphisms.…
Implicit representations of codimension-2 submanifolds and their prequantum structure
Albert Chern, Sadashige Ishida
This paper explores the geometry of the space of codimension-2 submanifolds. We implicitly represent these submanifolds by a class of complex-valued functions. We show that the spa…
Quadratic-Order Geodesics on Meshes
Yue Ruan, Albert Chern, Tzu-Mao Li +2
We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizatio…
L'Hopital rules for complex-valued functions in higher dimensions
Albert Chern, Sadashige Ishida
In calculus, l'Hopital's rule provides a simple way to evaluate the limits of quotient functions when both the numerator and denominator vanish. But what happens when we move beyon…