arXiv research

Calculates spinor heat flow using Gaussian-Grassmann integrals.

Quantum stochastic flow computes heat kernel traces for Ricci flat manifolds.

A new spinorial heat flow framework studies geometric degeneration on 3-manifolds.

Study the spectral flow of Dirac operators on spinor bundles.

Study quantum diffusion on spectral triples and spinor bundles.

The heat flow for Dirac-harmonic maps on Riemannian spin manifolds is a modification of the classical heat flow for harmonic maps by coupling it to a spinor. It was introduced by Chen, Jost, Sun, and Zhu as a tool to get a general existence program for Dirac-harmonic maps. For source manifolds with boundary they obtain…

Novel heat flow estimates on ALE manifolds for Schrödinger operators.

The problem of evaluating heat invariants can be computerized. Geometric symbol calculus of pseudodifferential operators is the main tool of such computerization.

Study reveals how to determine area and curvature from fluid flow resonances.

The paper studies parallel spinor flows on 3D Cauchy hypersurfaces and provides initial data characterizations.

Paper studies flows of spinor fields with flux for unified theories.

The purpose of this article is to study Ezra Getzler's approach to the Atiyah-Singer index theorem from the perspective of Alain Connes' tangent groupoid. We shall construct a "rescaled" spinor bundle on the tangent groupoid, define a convolution operation on its smooth, compactly supported sections, and explain how th…

The study explores highly supersymmetric backgrounds in 11D supergravity.

We establish, via geometric quantization of the supercotangent bundle sM of (M,g), a correspondence between its conformal geometry and those of the spinor bundle. In particular, the Kosmann Lie derivative of spinors is obtained by quantization of the comoment map, associated to the new Hamiltonian action of conf(M,g) o…

We show stability of pairs of Ricci flat metrics and parallel spinor fields with respect to the spinor flow, i.e. we show that the spinor flow with initial conditions near such pairs converges to a critical point with exponential speed. Moreover, we show stability of certain volume constrained critical points of the sp…

The paper connects Ricci flow and harmonic spinors, proving new inequalities.

We study the spinor flow on homogeneous spin manifolds. After providing the general setup we discuss the homogeneous spinor flow in dimension 3 and on almost abelian Lie groups in detail. As a further example the flag manifold in dimension 6 is treated.

Paper studies heat flow for maps on manifolds, avoiding singularities.

Study on biharmonic map heat flow with monotonicity formula.

The Liouville theorem is proven for V T-harmonic map heat flow.

Study torsion parallel spinors on Lorentzian 4-manifolds and their evolution flows.

Paper studies smoothness of bi-conformal heat flow on 4-manifolds.

On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, φ) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor φ. We investigate the basic properties of this functional and study its negative gradient f…

In this paper, we study two kind of L^2 norm preserved non-local heat flows on closed manifolds. We first study the global existence, stability and asymptotic behavior to such non-local heat flows. Next we give the gradient estimates of positive solutions to these heat flows.

The paper shows connections can be uniquely determined by their boundary data.

Heat flow fails to preserve concavity in curved spaces.

Bounds on Hessian of heat equation coupled with Ricci flow.

Extends heat kernel estimates for super Ricci flow.

Exponential rate of convergence for harmonic heat flow maps.

In this note, we establish certain regularity estimates for the spinor flow introduced and initially studied in \cite{AWW2016}. Consequently, we obtain that the norm of the second order covariant derivative of the spinor field becoming unbounded is the only obstruction for long-time existence of the spinor flow. This g…

The paper proves a Liouville theorem for heat flows on manifolds with specific curvature conditions.

We study the heat equation on time-dependent metric measure spaces (as well as the dual and the adjoint heat equation) and prove existence, uniqueness and regularity. Of particular interest are properties which characterize the underlying space as a super Ricci flow as previously introduced by the second author. Our ma…

Article proves Liouville theorem for heat equation in super Ricci flow.

Proves upper bounds for heat kernels evolving on manifolds.

New approach to heat flow for half-harmonic maps, related to minimal surfaces.

Paper studies heat flow for VT harmonic maps on compact manifolds.

We study perturbed Dirac operators of the form $D_s= D + s{\cal A} :Γ(E)\rightarrow Γ(F)$ over a compact Riemannian manifold $(X, g)$ with symbol $c$ and special bundle maps ${\cal A} : E\rightarrow F$ for $s>>0$. Under a simple algebraic criterion on the pair $(c, {\cal A})$, solutions of $D_sψ=0$ concentrate as $s\t…

We prove several differential Harnack inequalities for positive solutions to nonlinear backward heat equations with different potentials coupled with the Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear heat equation under the $\varepsilon$-Ricci flow on a closed surface. These new Harnac…

We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those Riemannian flows $M$ carrying non-trivial solutions to that equation in case $M$ is a local Riemannian product, a Sasakian manifold or 3-dimensional.

We present two initial graphs over the entire $\mathbb{R}^n$, $n \geq 2$ for which the mean curvature flow behaves differently from the heat flow. In the first example, the two flows stabilize at different heights. With our second example, the mean curvature flow oscillates indefinitely while the heat flow stabilizes. …

Study heat flow on changing surfaces, proving existence and uniqueness.

Paper defines a new functional for spinors on Euclidean manifolds.

Study proves short-term existence for harmonic maps under evolving metrics.

We establish global existence of smooth solutions to heat flow for Yang-Mills-Higgs functional on Kahler fibrations. As an application, we give a new proof of the key inequality for Mundet's Hitchin-Kobayashi correspondence theorem using the heat flow technique.

Paper proves estimates for heat and conjugate heat equations under Ricci flow, leading to monotonicity of parabolic frequencies.

The paper explores heat flow and constants on graphs, proving properties and proposing new concepts.

Extends gradient estimates for heat equation under Finsler geometric flows.

Global existence and convergence of heat flow for p-harmonic maps.