Related papers: Spherical harmonics with maximal Lp (2<p<=6) norm …

The goal of this work is to prove the regularity of certain quasi-plurisubharmonic upper envelopes. Such envelopes appear in a natural way in the construction of hermitian metrics with minimal singularities on a big line bundle over a…

We use sphericalization to study the Dirichlet problem, Perron solutions and boundary regularity for p-harmonic functions on unbounded sets in Ahlfors regular metric spaces. Boundary regularity for the point at infinity is given special…

We prove that local weak solutions of the orthotropic $p-$harmonic equation are locally Lipschitz, for every $p\ge 2$ and in every dimension. More generally, the result holds true for more degenerate equations with orthotropic structure,…

We establish new strong lower bounds on the (subnormal) subgroup growth of a large class of groups. This includes the fundamental groups of all finite-volume hyperbolic 3-manifolds and all (free non-abelian)-by-cyclic groups. The lower…

We show that PSL(2,Z[1/p]) admits a combing with bounded asynchronous width, and use this combing to show that PSL(2,Z[1/p]) has an exponential Dehn function. As a corollary, PSL(2,Z[1/p]) has solvable word problem and is not an automatic…

For a class of reducible Hamiltonian partial differential equations (PDEs) with arbitrary spatial dimensions, quantified by a quadratic polynomial with time-dependent coefficients, we present a comprehensive classification of long-term…

For a measure on a subset of the complex plane we consider $L^p$-optimal weighted polynomials, namely, monic polynomials of degree $n$ with a varying weight of the form $w^n = {\rm e}^{-n V}$ which minimize the $L^p$-norms, $1 \leq p \leq…

We consider time-harmonic acoustic scattering by a compact sound-soft obstacle $\Gamma\subset \mathbb{R}^n$ ($n\geq 2$) that has connected complement $\Omega := \mathbb{R}^n\setminus \Gamma$. This scattering problem is modelled by the…

We develop an optimal regularity theory for $L^p$-viscosity solutions of fully nonlinear uniformly elliptic equations in nondivergence form whose gradient growth is described through a Hamiltonian function with measurable and possibly…

We establish the $L^p(\mathbb{R}^3)$ boundedness of the helical maximal function for the sharp range $p>3$. Our results improve the previous known bounds for $p>4$. The key ingredient is a new microlocal smoothing estimate for averages…

We study partial regularity for nondegenerate parabolic systems of double phase type, where the growth function is given by $H(z,s)=s^p+a(z)s^q$, $z=(x,t)\in\Omega_T$, with $\tfrac{2n}{n+2}<p\le q$ and $a(z)$ a nonnegative…

We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their area. This also allows us to prove a new lower bound on the…

We study the relationship between $L^\infty$ growth of eigenfunctions and their $L^2$ concentration as measured by defect measures. In particular, we characterize the defect measures of any sequence of eigenfunctions with maximal $L^\infty$…

We consider weak distributional solutions to the equation $-\Delta_pu=f(u)$ in half-spaces under zero Dirichlet boundary condition. We assume that the nonlinearity is positive and superlinear at zero. For $p>2$ (the case $1<p\leq2$ is…

Motivated by the problem of the small-scale sign distribution of Laplace eigenfunctions, we introduce a strong notion of sign-balance for (eigen)functions, and prove that random eigenfunctions are sign-balanced above a precisely determined…

In this paper we generalize the main result of [4] for manifolds that are not necessarily Einstein. In fact, we obtain an upper bound for the volume of a locally volume-minimizing closed hypersurface $\Sigma$ of a Riemannian 5-manifold $M$…

Semilinear stochastic partial differential equations on bounded domains $\mathscr{D}$ are considered. The semilinear term may have arbitrary polynomial growth as long as it is continuous and monotone except perhaps near the origin. Typical…

We begin by recalling the definition of nonnegative quasinearly subharmonic functions on locally uniformly homogeneous spaces. Recall that these spaces and this function class are rather general: among others subharmonic, quasisubharmonic…

A class of subharmonic functions represented by the modified kernels are proved to have the growth estimates $u(z)= o(y^{1-\alpha}|z|^{m+\alpha})$ at infinity in the upper half plane ${\bf C}_{+}$, which generalizes the growth properties of…

We establish the equivalence between superharmonic functions and locally renormalized solutions for the elliptic measure data problems with $(p, q)$-growth. By showing that locally renormalized solutions are essentially bounded below and…