Mathematische Annalen最新文献

We investigate basic properties of mappings of finite distortion (f:X rightarrow mathbb {R}^2), where X is any metric surface, i.e., metric space homeomorphic to a planar domain with locally finite 2-dimensional Hausdorff measure. We introduce lower gradients, which complement the upper gradients of Heinonen and Koskela, to study the distortion of non-homeomorphic maps on metric spaces. We extend the Iwaniec-Šverák theorem to metric surfaces: a non-constant (f:X rightarrow mathbb {R}^2) with locally square integrable upper gradient and locally integrable distortion is continuous, open and discrete. We also extend the Hencl-Koskela theorem by showing that if f is moreover injective then (f^{-1}) is a Sobolev map.

We consider Bochner–Riesz means on weighted (L^p) spaces, at the critical index (lambda (p)=d(frac{1}{p}-frac{1}{2})-frac{1}{2}). For every (A_1)-weight we obtain an extension of Vargas’ weak type (1, 1) inequality in some range of (p>1). To prove this result we establish new endpoint results for sparse domination. These are almost optimal in dimension (d= 2); partial results as well as conditional results are proved in higher dimensions. For the means of index (lambda _*= frac{d-1}{2d+2}) we prove fully optimal sparse bounds.

Necessary and sufficient conditions are presented for a fractional Orlicz-Sobolev space on ({mathbb {R}}^n) to be continuously embedded into a space of uniformly continuous functions. The optimal modulus of continuity is exhibited whenever these conditions are fulfilled. These results pertain to the supercritical Sobolev regime and complement earlier sharp embeddings into rearrangement-invariant spaces concerning the subcritical setting. Classical embeddings for fractional Sobolev spaces into Hölder spaces are recovered as special instances. Proofs require novel strategies, since customary methods fail to produce optimal conclusions.

In this paper we continue the study on intrinsic Harnack inequality for non-homogeneous parabolic equations in non-divergence form initiated by the first author in Arya (Calc Var Partial Differ Equ 61:30–31, 2022). We establish a forward-in-time intrinsic Harnack inequality, which in particular implies the Hölder continuity of the solutions. We also provide a Harnack type estimate on global scale which quantifies the strong minimum principle. In the time-independent setting, this together with Arya (2022) provides an alternative proof of the generalized Harnack inequality proven by the second author in Julin (Arch Ration Mech Anal 216:673–702, 2015).

In this paper we introduce bilinear Bochner–Riesz means associated with convex domains in the plane ({mathbb {R}}^2) and study their (L^p)-boundedness properties for a wide range of exponents. One of the important aspects of our proof involves the use of bilinear Kakeya maximal function in the context of bilinear Bochner–Riesz problem. This amounts to establishing suitable (L^p)-estimates for the later. We also point out some natural connections between bilinear Kakeya maximal function and Lacey’s bilinear maximal function.

We show that we can retrieve a Yang–Mills potential and a Higgs field (up to gauge) from source-to-solution type data associated with the classical Yang–Mills–Higgs equations in Minkowski space ({mathbb {R}}^{1+3}). We impose natural non-degeneracy conditions on the representation for the Higgs field and on the Lie algebra of the structure group which are satisfied for the case of the Standard Model. Our approach exploits the non-linear interaction of waves generated by sources with values in the centre of the Lie algebra showing that abelian components can be used effectively to recover the Higgs field.

We unveil instances where nonautonomous linear systems manifest distinct nonuniform (mu )-dichotomy spectra despite admitting nonuniform ((mu , varepsilon ))-kinematic similarity. Exploring the theoretical foundations of this lack of invariance, we discern the pivotal influence of the parameters involved in the property of nonuniform (mu )-dichotomy such as in the notion of nonuniform ((mu , varepsilon ))-kinematic similarity. To effectively comprehend these dynamics, we introduce the stable and unstable optimal ratio maps, along with the (varepsilon )-neighborhood of the nonuniform (mu )-dichotomy spectrum. These new concepts provide a framework for understanding scenarios governed by the noninvariance of the nonuniform (mu )-dichotomy spectrum.

This paper provides a systematization of some recent results in homology of algebras. Our main theorem gives criteria under which the homology of a diagram algebra is isomorphic to the homology of the subalgebra on diagrams having the maximum number of left-to-right connections. From this theorem, we deduce the ‘invertible-parameter’ cases of the Temperley–Lieb and Brauer results of Boyd–Hepworth and Boyd–Hepworth–Patzt. We are also able to give a new proof of Sroka’s theorem that the homology of an odd-strand Temperley–Lieb algebra vanishes, as well as an analogous result for Brauer algebras and an interpretation of both results in the even-strand case. Our proofs are relatively elementary: in particular, no auxiliary chain complexes or spectral sequences are required. We briefly discuss the relationship to cellular algebras in the sense of Graham–Lehrer.

We study sparse domination for operators defined with respect to an atomic filtration on a space equipped with a general measure (mu ). In the case of Haar shifts, (L^p)-boundedness is known to require a weak regularity condition, which we prove to be sufficient to have a sparse domination-like theorem. Our result allows us to characterize the class of weights where Haar shifts are bounded. A surprising novelty is that said class depends on the complexity of the Haar shift operator under consideration. Our results are qualitatively sharp.

We commonly refer to an extremal Kähler metric with finitely many singularities on a compact Riemann surface as a metric where the Hessian of the curvature of the Metric is Umbilical, known as an HCMU metric. In this study, we specifically classify non-CSC HCMU metrics on the K-surfaces (S^2_{{alpha }}) and (S^2_{{alpha ,beta }}).