arXiv research

The paper proves Liouville rigidity for Hessian equations, characterizing geometric conditions for constant solutions.

Paper derives estimates for Hessian equations under concavity assumptions.

Arnold-Liouville systems cannot be bi-Hamiltonian generically.

We study analytic properties of harmonic maps from Riemannian polyhedra into CAT($κ$) spaces for $κ\in\{0,1\}$. Locally, on each top-dimensional face of the domain, this amounts to studying harmonic maps from smooth domains into CAT($κ$) spaces. We compute a target variation formula that captures the curvature bound in…

We consider the problem $\mathbf{P_{curve}}$ of minimizing $\int \limits_0^L \sqrt{ξ^2 + κ^2(s)} \, {\rm d}s$ for a curve $\mathbf{x}$ on $\mathbb R$ with fixed boundary points and directions. Here the total length $L\geq 0$ is free, $s$ denotes the arclength parameter, $κ$ denotes the absolute curvature of $\mathbf{x}…

The paper explores the $L^1$-Liouville property on graphs and its connections to stochastic completeness.

We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof of the classical Liouville theorem for harmonic functions. Applications of the …

Study explores Liouville's theorem and SLP for harmonic functions on cones and surfaces.

Equal diagonal energies proven on Liouville surfaces.

A 'Liouville structure' is a structure isomorphic to a cotangent vector fibration. A Liouville structure is an essential ingredient of every variational formulation of a physical theory. For reasons of interpretation the Liouville structure can not be replaced by the corresponding cotangent fibration. We give a precise…

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

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

Study Liouville action for harmonic maps between Riemann surfaces.

We study simple root flows and Liouville currents for Hitchin representations. We show that the Liouville current is associated to the measure of maximal entropy for a simple root flow, derive a Liouville volume rigidity result, and construct a Liouville pressure metric on the Hitchin component.

The paper classifies invariant operators and proves a Liouville theorem.

Study non-Weinstein Liouville geometry via hyperbolic dynamics, proving rigidity results.

The universal Liouville action equals the renormalized volume of a hyperbolic 3-manifold.

Study shows that deformed Liouville metrics on tori remain Liouville.

Proves a Liouville-type theorem for p-Laplacian on manifolds.

Study Liouville theorem for specific harmonic maps.

The paper investigates Liouville type theorems for various harmonic forms on Riemannian manifolds.

Optimal Liouville theorem for half-Euclidean space equations.

Generative model improved using Liouville PDE-based sliced-Wasserstein flow.

The paper derives Liouville theorems for various generalized maps on Riemannian manifolds.

This note provides a new proof of the real analyticity of the Liouville map.

Study Liouville theorems for harmonic maps along ancient super Ricci flows.

Liouville domains have become central objects in symplectic and contact geometry. However, the auxiliary data they involve --- namely, Liouville forms --- and the non-compactness of their completions generate some inconvenience. The notion of ideal Liouville domains is designed to suppress these awkward aspects and to …

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

The paper extends Liouville's theorem to calibrated geometries in various dimensions.

The paper proves a Liouville theorem for specific harmonic maps with free boundary.

Liouville entropy increases strictly along Ricci flow on surfaces.

Improved Liouville theorems for ancient solutions to V-harmonic map heat flows.

New method shows some 3D shapes can't be filled in certain ways.

Four geometries govern sequential and distribution-free inference.

The paper classifies solutions to a Liouville equation on a half-space with a specific boundary condition.

Researchers found a Weyl law for Liouville quantum gravity eigenvalues.

Special Liouville metrics with Ricci-like conditions are determined by elliptic functions.

We study the Liouville action for quasi-Fuchsian groups with parabolic and elliptic elements. In particular, when the group is Fuchsian, the contribution of elliptic elements to the classical Liouville action is derived in terms of the Bloch-Wigner functions. We prove the first and second variation formulas for the cla…

Ancient Lagrangian flows get limited convex solutions.

Study proves Liouville theorem for specific curvature equations with boundary conditions.

The paper establishes gradient estimates and Liouville theorems for Φ-Laplacian equations on Riemannian manifolds.

The paper proves Mabuchi solitons and constants on Fano admissible manifolds.

Paper provides criteria to detect non-admissible quandles via coloring.

Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and analytic aspects of the resulting Euler-Lagrange equations, culminating in a blo…

Paper proves a Liouville theorem for solitons with constant curvature.

New GLPs split Lévy bridges into non-overlapping subprocesses.

In this short paper we study $L_f^p$-Liouville property with $0<p<1$ for nonnegative $f$-subharmonic functions on a complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ with $\mathrm{Ric}_f^m$ bounded below for $0<m\leq\infty$. We prove a sharp $L_f^p$-Liouville theorem when $0<m<\infty$. We also prove an $…

In this article we will construct the Liouville parametrization of the triaxial ellipsoid. In the literature quadrics are given as examples of Liouville surfaces, yet no one gives such a parametrization. For this we introduce the generalized Jacobi amplitude as inverse of the elliptic integral of the third kind.