arXiv research

Sharp estimates for heat flow on nonconvex domains.

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

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

Quantitative Sobolev extensions lead to Neumann heat kernel bounds.

Study on heat trace expansion for thermoelastic Dirichlet-to-Neumann map.

We study new heat kernel estimates for the Neumann heat kernel on a compact manifold with positive Ricci curvature and convex boundary. As a consequence, we obtain new lower bounds for the Neumann eigenvalues which are consistent with Weyl's asymptotics.

In this paper we will prove a maximum principle for the solutions of linear parabolic equation on complete non-compact manifolds with a time varying metric. We will prove the convergence of the Neumann Green function of the conjugate heat equation for the Ricci flow in $B_k\times (0,T)$ to the minimal fundamental solut…

Study heat profiles and eigenfunctions using Brownian motion.

By using Hsu's multiplicative functional for the Neumann heat equation, a natural damped gradient operator is defined for the reflecting Brownian motion on compact manifolds with boundary. This operator is linked to quasi-invariant flows in terms of a integration by parts formula, which leads to the standard log-Sobole…

The paper compares heat kernels on manifolds with Robin boundary conditions.

Study heat flow on collapsing K3 surfaces, handling conic singularities.

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

The paper improves eigenvalue estimates for manifolds with Ricci curvature conditions.

Extends Onsager's conjecture to Besov spaces on manifolds with boundary.

Study on biharmonic map heat flow with monotonicity formula.

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

We study the heat trace asymptotics associated with the Steklov eigenvalue problem on a Riemannian manifold with boundary. In particular, we describe the structure of the Steklov heat invariants and compute the first few of them explicitly in terms of the scalar and mean curvatures. This is done by applying the Seeley …

We consider the Hodge Laplacian on manifolds with incomplete edge singularities, with infinite dimensional von Neumann spaces and intricate elliptic boundary value theory. We single out a class of its algebraic self-adjoint extensions. Our microlocal heat kernel construction for algebraic boundary conditions is guided …

In this paper, we prove long time existence and convergence results for a class of general curvature flows with Neumann boundary condition. This is the first result for the Neumann boundary problem of non Monge-Ampere type curvature equations. Our method also works for the corresponding elliptic setting.

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

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.

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.

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…

On a large class of Riemannian manifolds with boundary, some dimension-free Harnack inequalities for the Neumann semigroup is proved to be equivalent to the convexity of the boundary and a curvature condition. In particular, for $p_t(x,y)$ the Neumann heat kernel w.r.t. a volume type measure $μ$ and for $K$ a constant,…

Paper proves translating solutions for a specific flow in a product manifold.

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

Proves upper bounds for heat kernels evolving on manifolds.

Study proves mean curvature flow in GRW spacetimes with perpendicular boundary condition.

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

Calculates spinor heat flow using Gaussian-Grassmann integrals.

We study mean curvature flow of smooth, axially symmetric surfaces in $\mathbb{R}^3$ with Neumann boundary data. We show that all singularities at the first singular time must be of type I.

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…

This paper demonstrates existence for all time of mean curvature flow in Minkowski space with a perpendicular Neumann boundary condition, where the boundary manifold is a convex cone and the flowing manifold is initially spacelike. Using a blowdown argument, we show that under renormalisation this flow converges toward…

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.

Constructs index for elliptic operators using rapidly decaying kernels.

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

New method reveals corners of drum shapes.

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.

Proves estimates for Kähler-Ricci flow solutions.