arXiv research

In this paper, we study inextensible flows of non-null curves in E^n,1. We give necessary and sufficient conditions for inextensible flow of nonnull curves in E^n,1.

In this paper, we investigate the general formulation for inextensible flows of curves in En. The necessary and sufficient conditions for inextensible curve flow are expressed as a partial differential equation involving the curvatures.

In this paper, the general formulation for inextensible flows of curves on oriented surface in $\mathbb{R}^3$ is investigated. The necessary and sufficient conditions for inextensible curve flow lying an oriented surface are expressed as a partial differential equation involving the geodesic curvature and the geodesic…

In this paper, we study inextensible flows of partially null and pseudo null curves in E_1^4. We give neccessary and sufficent conditions for inextensible flows of partially null and pseudo null curves in E_1^4

Study inextensible flows of curves in 4D pseudo-Galilean space and defines energy functions.

We study the evolution of closed inextensible planar curves under a second order flow that decreases the $p$-elastic energy. A short time existence result for $p \in (1,\infty)$ is obtained via a minimizing movements method. For $p = 2$, that is in the case of the classic elastic energy, long-time existence is retrieve…

We develop a theory of planar, origin-symmetric, convex domains that are inextensible with respect to lattice covering, that is, domains such that augmenting them in any way allows fewer domains to cover the same area. We show that origin-symmetric inextensible domains are exactly the origin-symmetric convex domains wi…

A new model for simulating cloth manipulation in robots, accurate to within 1cm.

We study the geometry of the inextensible string (the whip) and its discrete approximation (the chain). In the absence of gravity, both motions represent geodesic motions on certain manifolds. We show how the motion of the chain converges to that of a whip, and how the curvature of the chain's configuration space conve…

Develops a lifting theory for exponential maps in semi-Riemannian geometry.

In this paper, we get the time evolution equations of the curvature and torsion of the evolving spacelike curves in the Minkowski space. Also, we give inextensible evolutions of timelike ruled surfaces that are produced by the timelike normal and spacelike binormal vector fields of spacelike curve and derive the necess…

Unified theory solves strain compatibility and elasticity of origami metamaterials.

In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution …

Study of convergence in Lorentzian spacetimes using temporal functions.

Frustration causes buckling-like behavior in tubular foldable mechanisms.

New flows introduced for symplectic geometry.

The paper examines Ricci flows with closed and smooth tangent flows, proving uniqueness and characterizing ancient flows.

Proves uniqueness of geometric flow in various Riemannian manifolds.

Study of twisted Calabi flow connecting J-flow and Calabi flow on Kähler manifolds.

Investigate scalar curvature under geometric flows

Streets and Tian introduced pluriclosed flow and symplectic curvature flow in recent years. Here we construct a curvature flow to unify these two flows. We show the short time existence of our flow and exhibit an obstruction to long time existence.

We consider four extended Ricci flow systems---that is, Ricci flow coupled with other geometric flows---and prove dynamical stability of certain classes of stationary solutions of these flows. The systems include Ricci flow coupled with harmonic map flow (studied abstractly and in the context of Ricci flow on warped pr…

The article calculates the $\mathbb{F}$-convergence rate for Ricci flows with closed and smooth tangent flows.

Paper introduces Tensor Gauge Flow Models for better data encoding.

Study K-R flow on Hirzebruch surfaces, showing tangent flows are K-R flows with orbifold singularities.

Ancient curve shortening flows have entropy and curvature bounds equivalent.

The study disproves rotating ancient flows in 4D space.

Simplifies residual flows to make flow-based modeling more practical.

Existence of translating solutions shown for curve diffusion flow.

Modeling bone microarchitecture adaptation using geometric flows.

Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a generalization of planar flows. Sylvester normalizing flows remove the well-known single…

The Hodge star mean curvature flow on a 3-dimension Riemannian or pseudo-Riemannian manifold, the geometric Airy flow on a Riemannian manifold, the Schrodingier flow on Hermitian manifolds, and the shape operator curve flow on submanifolds are natural non-linear dispersive curve flows in geometric analysis. A curve flo…

In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijectiv…

The study examines mass drop and multiplicity in mean curvature flow.

We explore the harmonic-Ricci flow---that is, Ricci flow coupled with harmonic map flow---both as it arises naturally in certain principal bundle constructions related to Ricci flow and as a geometric flow in its own right. We demonstrate that one natural geometric context for the flow is a special case of the locally …

Using the conformally invariant Cotton tensor, we define a geometric flow, the "Cotton flow", which is exclusive to three dimensions. This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to the Yamabe flow, the latter being a flow within a conformal class. We define an en…

The paper studies mean curvature flow in a Ricci flow background with extended Ricci flow.

Mean curvature flow is not a gradient flow on two nondegenerate metric spaces.

New derivation of Type IIA flow metrics.

Survey of geometric flows from unified string theories.

SurVAE Flows combine VAEs and flows using surjective transformations.

Study describes global existence and convergence of flows on surfaces and fibrations.

Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.

By the method of discrete Morse flows, we construct an energy reducing multiple-valued function flow. The flow we get is Holder continuous with respect to the L-2 norm. We also give another way of constructing flows in some special cases, where the flow we get behaves like ordinary heat flow.

Higher Gauge Flow Models integrate higher geometry and symmetries into Generative Flow Models.

A new geometric flow $K$-flow on 3-manifolds shrinks or preserves homogeneous spheres.

New perspective on G2-structures flow from DeTurck Laplacian.

Study $G_2$-flows reducing to complex geometry flows, focusing on $G_2$-anomaly and $G_2$-Laplacian coflow.