Annali di Matematica Pura ed Applicata最新文献

In this paper, we mainly investigate the critical points of solutions to the semilinear elliptic equations with Neumann and Robin boundary conditions on two-dimensional convex domains of Riemannian surfaces. Precisely, under some certain convexity assumptions for domains (Omega ), we show the non-degeneracy of critical points of solutions to the corresponding boundary problem in (Omega subset {mathbb {S}}^2,{mathbb {R}}^2) or ({mathbb {H}}^2) by using Chen & Huang’s comparison technique (Invent Math. 67:253-259, 1982), and prove the uniqueness of critical points by continuity method and topological degree argument.

In this paper, we construct a one-parameter family of minimal surfaces in the Euclidean 3-space of arbitrarily high genus and with three ends. Each member of this family is immersed, complete and with finite total curvature. Another interesting property is that the symmetry group of the genus k surfaces (Sigma _{k,t}) is the dihedral group with (4(k+1)) elements. Moreover, in particular, for (|t|=1) we find the family of the Costa–Hoffman–Meeks embedded minimal surfaces, which have two catenoidal ends and a middle flat end. Among the non-embedded examples obtained, there are noncongruent minimal surfaces, with the same symmetry group and conformal structure, as we have in Ramos Batista (Tohoku Math. J. (2) 56(2):237–254, 2004).

We provide a splitting criterion for supervector bundles over the projective superspaces (mathbb {P}^{n|m}). More precisely, we prove that a rank p|q supervector bundle on (mathbb {P}^{n|m}) with vanishing intermediate cohomology is isomorphic to the direct sum of even and odd line bundles, provided that (n ge 2). For (n=1) we provide an example of a supervector bundle that cannot be written as a sum of line bundles.

For each (0<alpha <frac{1}{2}), there exists a Bayer–Lahoz–Macrì–Stellari inducing Bridgeland stability condition (sigma (alpha )) on a Kuznetsov component (textrm{Ku}(Q)) of the smooth quadric threefold Q. We obtain the non-emptiness of the moduli space (M_{sigma (alpha )}([{mathcal {P}}_{x}])) of (sigma (alpha ))-semistable objects in (textrm{Ku}(Q)) with the numerical class ([{mathcal {P}}_{x}]), where ({mathcal {P}}_{x}in textrm{Ku}(Q)) is the projection sheaf of the skyscraper sheaf at a closed point (xin Q). We show that the moduli space ({overline{M}}_{Q}({textbf{v}})) of Gieseker semistable sheaves with Chern character ({textbf{v}}=textrm{ch}({mathcal {P}}_{x})) is smooth and irreducible of dimension four, and prove that the moduli space (M_{sigma (alpha )}([{mathcal {P}}_{x}])) is isomorphic to ({overline{M}}_{Q}({textbf{v}})). As an application, we show that the quadric threefold Q can be reinterpreted as a Brill–Noether locus in the Bridgeland moduli space (M_{sigma (alpha )}([{mathcal {P}}_{x}])). In the appendices, we show that the moduli space (M_{sigma (alpha )}([S])) contains only one single point corresponding to the spinor bundle S and give a Bridgeland moduli interpretation for the Hilbert scheme of lines in Q.

In this paper, we establish a connection between Dunkl analysis and slice analysis in the setting of Clifford algebras. Specifically, we show that a Clifford algebra-valued function is slice if, and only if, it belongs to the kernel of the Dunkl-spherical Dirac operator and that a slice function is slice regular if, and only if, it lies in the kernel of the Dunkl-Cauchy-Riemann operator for a suitable parameter. Based on this correspondence and the inverse Dunkl intertwining operator, we propose a new method to construct a family of classical monogenic functions from a given holomorphic function, in the spirit of Fueter’s theorem.

A finite group G is called uniformly semi-rational if there exists an integer r such that the generators of every cyclic subgroup (langle x rangle ) of G lie in at most two conjugacy classes, namely (x^G) or ((x^r)^G). In this paper, we provide a classification of uniformly semi-rational non-abelian simple groups with particular focus on alternating groups.

In his beautiful book Singular Integrals and Differentiability Properties of Functions, E.M. Stein introduces Marcinkiewicz integral as an alternative to the differentiation theorem to illustrate (literally quoting from [1, Ch.I, Sect.2.3]) “the principle that a general point of a measurable set is almost completely surrounded by other points of the set”. We want to explore the theme summarised by this Stein’s sentence, using the notion of superdensity point.

In this paper we study the influence of an absorption term of power type on the regularity and time behavior of the solutions to a class of nonlinear parabolic problems. We will show that important and unexpected changes occur. For example, in absence of a forcing term it can produce an immediate boundedness in cases when it is well known that, in absence of such a lower-order term, the solutions remain unbounded. Moreover, we prove that regularization phenomena appear also in presence of forcing terms.

The translation operator (T^A) associated with the special affine Fourier transform (SAFT) (mathscr {F}_A) is introduced from harmonic analysis point of view. The analogues of Wendel’s theorem, Wiener theorem, Wiener-Tauberian theorem and Bernstein type inequality in the context of the SAFT are established. The shift invariant space (V_A) associated with the special affine Fourier transform is introduced and studied along with sampling problems.

In this note, by establishing a priori estimate, we reprove the optimal Liouville theorem for a large class of subcritical semilinear elliptic equations on Riemannian manifolds with nonnegative Ricci curvature. Based on the classical Bernstein method, our proofs rely on the new auxiliary functions constructed in Lu (Logarithmic gradient estimate and universal bounds for semilinear elliptic equations revisited) and the lower bounds of nonnegative superharmonic functions inspired by Catino and Monticelli (J Eur Math Soc, 2024. https://doi.org/10.4171/jems/1484), Serrin and Zou (Acta Math 189(1):79–142, 2002) and Wu (Liouville theorem for one kind of elliptic equations on complete Riemannian manifold). Besides recovering the classical results, our theorems have three advantages as follows: first, we do not need the nonlinear terms to be superlinear; second, we find a new Liouville property, which claims the non-existence of bounded solutions for a class of critical equations; third, using the concept of Bakry-Émery Ricci curvature, we relax the conditions on the coefficient functions to consider Lane-Emden equations with gradient term. These conditions are optimal for the validity of the Liouville property considered in this work.