Annali di Matematica Pura ed Applicata最新文献

We consider biconservative surfaces in (text {Sol}_3), find their local equations, and then show that all biharmonic surfaces in this space are minimal.

We establish the global well-posedness for generalized derivative KdV equations with small rough data in specific modulation spaces (M_{2,1}^{1/m}) by the method of smoothing effect estimates combined with the frequency-uniform decomposition. Furthermore, we demonstrate that the mapping from data to solutions is not (C^{m+1}) continuous in (M_{2,1}^{s}) for (s<1/m), indicating the sharpness of the well-posedness result.

We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible bounded symmetric domain with respect to the Bergman metrics. In this direction, we show that images of (nonempty) affine-linear sections of the complex unit ball must be the intersections of the image of the holomorphic isometry with certain affine-linear subspaces. We also construct a surjective holomorphic submersion from a certain subdomain of the target bounded symmetric domain onto the complex unit ball such that the image of the holomorphic isometry lies inside the subdomain and the holomorphic isometry is a global holomorphic section of the holomorphic submersion. This construction could be generalized to any holomorphic isometry between bounded symmetric domains with respect to the canonical Kähler metrics. Using some classical results for complex-analytic subvarieties of Stein manifolds, we have obtained further geometric results for images of such holomorphic isometries.

We give (L^p) estimates for the second derivatives of weak solutions to the Dirichlet problem for equation (textrm{div}({textbf{A}}nabla u) = f) in (Omega subset {mathbb {R}}^d) with Sobolev coefficients. In particular, for (fin L^2(Omega ) bigcap L^s(Omega ))

In this paper, we study relative Rota–Baxter operators of weight 0 on groups and give various examples. In particular, we propose different approaches to study Rota–Baxter operators of weight 0 on groups and Lie groups. We establish various explicit relations among relative Rota–Baxter operators of weight 0 on groups, pre-groups, braces, set-theoretic solutions of the Yang–Baxter equation and T-structures.

In this paper we study strongly singular problems with Dirichlet boundary condition on bounded domains given by

where (1<p<N), (p<q<p^*=frac{Np}{N-p}), (0 le mu (cdot ) in L^infty (Omega )), (1<r) and (hin L^1(Omega )) with (h(x)>0) for a.a. (xin Omega ). Since the exponent r is larger than one, the corresponding energy functional is not continuous anymore and so the related Nehari manifold

is not closed in the Musielak-Orlicz Sobolev space (W^{1,mathcal {H}}_0(Omega )). Instead we are minimizing the energy functional over the constraint set

which turns out to be closed in (W^{1,mathcal {H}}_0(Omega )) and prove the existence of at least one weak solution. Our result is even new in the case when the weight function (mu ) is away from zero.

In this note we study the stability of the Kobayashi distances (under two types of scaling processes) on Levi corank one domains. As an application, based on local uniform estimates of the Kobayashi metrics and distances, we show that the Levi corank one domains are Gromov hyperbolic with respect to the Kobayashi distance.

In this paper, we provide a systematic and constructive description of Vaisman structures on certain principal elliptic bundles over complex flag manifolds. From this description, we explicitly classify homogeneous l.c.K. structures on compact homogeneous Hermitian manifolds using elements of representation theory of complex simple Lie algebras. Moreover, we also describe using Lie theory all homogeneous solutions of the Hermitian-Einstein-Weyl equation on compact homogeneous Hermitian-Weyl manifolds. As an application, we provide a huge class of explicit (nontrivial) examples of such structures on homogeneous Hermitian manifolds, these examples include elliptic bundles over full flag manifolds, elliptic bundles over Grassmannian manifolds, and 8-dimensional compact locally conformal hyperKähler manifolds.

We will provide a complete description of the space (M(X_F,X_G)) of pointwise multipliers between two Calderón–Lozanovskiĭ spaces (X_F) and (X_G) built upon a rearrangement invariant space X and two Young functions F and G. Meeting natural expectations, the space (M(X_F,X_G)) turns out to be another Calderón–Lozanovskiĭ space (X_{G ominus F}) with (G ominus F) being the appropriately understood generalized Young conjugate of G with respect to F. Nevertheless, our argument is not a mere transplantation of existing techniques and requires a rather delicate analysis of the interplay between the space X and functions F and G. Furthermore, as an example to illustrate applications, we will solve the factorization problem for Calderón–Lozanovskiĭ spaces. All this not only complements and improves earlier results (basically giving them the final touch), but also confirms the conjecture formulated by Kolwicz, Leśnik and Maligranda in [Pointwise multipliers of Calderón–Lozanovskiĭ spaces, Math. Nachr. 286 (2012), no. 8-9, 876–907]. We will close this work by formulating a number of open questions that outline a promising panorama for future research.

Kaneko and Yamamoto introduced a convoluted variant of multiple zeta values (MVZs) around 2016. In this paper, we will first establish some explicit formulas involving these values and their alternating version by using iterated integrals, which enable us to derive some explicit relations of the multiple polylogarithm (MPL) functions. Next, we define convoluted multiple t-values and multiple mixed values (MMVs) as level two analogs of convoluted MZVs, and, similar to convoluted MZVs, use iterated integrals to find some relations of these level two analogs. We will then consider the parametric MPLs and the parametric multiple harmonic (star) sums, and extend the Kaneko-Yamamoto’s “integral-series” identity of MZVs to MPLs and MMVs. Finally, we will study multiple integrals of MPLs and MMVs by generalizing Yamamoto’s graphical representations to multiple-labeled posets.