10 citations · 10 across the 7 of their papers we have counts for
7 papers
Ricci curvature for fluid models on the torus via Zeitlin's quantization
Sadashige Ishida, Alex Suri
Ricci curvature measures the average stability of geodesics under transverse perturbations, but how it should be defined in infinite dimensions is often unclear. This paper propose…
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…
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…
Symplectic structures on the space of space curves
Martin Bauer, Sadashige Ishida, Peter W. Michor
We present symplectic structures on the shape space of unparameterized space curves that generalize the classical Marsden-Weinstein structure. Our method integrates the Liouville 1…
Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation
Sadashige Ishida, Hugo Lavenant
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when t…
Area formula for spherical polygons via prequantization
Albert Chern, Sadashige Ishida
We present a formula for the signed area of a spherical polygon via prequantization. In contrast to the traditional formula based on the Gauss-Bonnet theorem that requires measurin…
Hidden Degrees of Freedom in Implicit Vortex Filaments
Sadashige Ishida, Chris Wojtan, Albert Chern
This paper presents a new representation of curve dynamics, with applications to vortex filaments in fluid dynamics. Instead of representing these filaments with explicit curve geo…