arXiv research

Extends strong comparison principle for p-harmonic functions in Carnot-Caratheodory spaces.

Local Lipschitz continuity of sub-elliptic harmonic maps into CAT(0) spaces proved.

We prove a version of differential Harnack inequality for a family of sub-elliptic diffusions on Sasakian manifolds under certain curvature conditions.

In this paper, we consider the principal eigenvalue problem for Hormander's laplacian on $R^n$. We also study a related semi-linear sub-elliptic equation in the whole $R^n$ and prove that under a suitable condition, we have infinite many positive solutions of the problem.

We give dimension-free regularity conditions for a class of possibly degenerate sub-elliptic equations in the Heisenberg group exhibiting super-quadratic growth in the horizontal gradient; this solves an issue raised by Manfredi & Mingione (Math. Ann. 2007) where only dimension dependent bounds for the growth exponent …

Our main aim is to present a geometrically meaningful formula for the fundamental solutions to a second order sub-elliptic differential equation and to the heat equation associated with a sub-elliptic operator in the sub-Riemannian geometry on the unit sphere $\mathbb S^3$. Our method is based on the Hamiltonian approa…

Researchers find second-order estimates for $p$-Laplacian in RCD spaces.

Study improves Reilly's inequality for $p$-Laplacian on submanifolds.

The paper defines new constants for $p$-Laplacian on manifolds.

The study finds bounds for the first eigenvalue of the p-Laplacian on submanifolds.

Study eigenvalues of p-Laplacian on quaternionic Kähler manifolds.

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

Study p-Laplacian equation on Riemannian manifolds with positive Ricci curvature.

Sharp lower bound for $p$-Laplacian eigenvalue on non-compact manifolds.

Study eigenvalues of p-Laplacian on Kähler manifolds, proving lower bounds.

Estimates eigenvalue of p-Laplacian on curved spaces.

Study on p-Laplacian problems with critical exponent, focusing on existence of solutions.

Paper proves inequality for p-Laplacian eigenvalues on curved spaces.

Sharp Talenti-type comparison theorem for p-Laplacian on RCD(K,N) spaces.

Study eigenvalues of p-Laplacian on differential forms.

Given a Finsler manifold $(M,F)$, it is proved that the first eigenvalue of the Finslerian $p$-Laplacian is bounded above by a constant depending on $\ p$, the dimension of $M$, the Busemann-Hausdorff volume and the reversibility constant of $(M,F)$. For a Randers manifold $(M,F:=\sqrt{g}+β)$, where $g$ is a Riemannian…

Study eigenvalues of a generalized p-Laplacian on forms.

In this paper, we establish gradient estimates for positive solutions to the following equation with respect to the $p$-Laplacian $Δ_{p}u=-λ|u|^{p-2}u$ with $p>1$ on a given complete Riemannian manifold. Consequently, we derive upper bound estimates of the first nontrivial eigenvalue of the $p$-Laplacian.

The paper studies eigenvalues and Cheeger constants on symmetric graphs.

Study eigenvalues of p-Laplacian on manifolds with Robin boundary conditions.

The paper studies how the first eigenvalue of a weighted p-Laplacian changes over time on Riemannian manifolds.

Study improves eigenvalue bounds on Kähler manifolds.

The paper confirms a Weyl law for the p-Laplacian on closed Riemannian manifolds.

The p-Laplacian Transformer improves transformer models by assigning higher attention weights to tokens in close proximity.

Researchers prove zero solutions for certain p-Laplacian equations in convex cones.

We prove the sharp estimate on the first nonzero eigenvalue of the p-laplacian on a compact Riemannian manifold with nonnegative Ricci curvature and possibly with convex boundary (in this case we assume Neumann b.c. on the p-laplacian). The proof is based on a gradient comparison theorem. We will also charachterize the…

The paper examines geometric properties of domains for the p-Laplacian in Euclidean and hyperbolic spaces.

Paper generalizes graph Laplacian to hypergraphs for semi-supervised learning.

Study finds bounds for fundamental tone on special Riemannian manifolds.

The paper proves existence and growth estimates for inverse mean curvature flow and related $p$-Laplacian Green kernel decay.

The paper finds lower bounds for the first eigenvalue of p-Laplacian in specific manifolds.

The paper proves gradient estimates for a weighted p-Laplacian equation on Riemannian manifolds.

We discuss the behavior of $(λ_{1. p}(M))^{1/p}$ with respect to the Gromov-Hausdorff topology and the variable $p$, where $λ_{1, p}(M)$ is the first positive eigenvalue of the $p$-Laplacian on a compact Riemannian manifold $M$. Applications include new estimates for the first eigenvalues of the $p$-Laplacian on Rieman…

This paper approximates $p$-resistance for multi-class graph clustering.

Smooth solutions up to evolving free boundaries for degenerate equations.

We establish lower bounds for the first non-zero eigenvalue for the natural geometric sub-elliptic Laplacian operator defined on sub-Riemannian manifolds of step 2 that satisfy a positive curvature condition. The methods are very general and can be applied even when the sub-Riemannian geometry has considerable torsion.

The paper sets up eigenvalue comparison theorems for specific Laplacians on manifolds.

Sharp lower bounds for eigenvalues on specific manifolds proved.

Develops a Barta theorem for p-Laplacian on manifolds.

Derives an inequality for submanifolds in spheres.

Paper solves Minkowski problem for anisotropic p-torsional rigidity.

Gradient estimates for solutions to a p-Laplacian equation on Riemannian manifolds.

Sharp gradient estimates for a weighted p-Laplacian equation on metric measure spaces.