- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 09:07:47
5
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PM&vol=70&iss=3&update_since=2024-03-29
Portugaliae Mathematica
Port. Math.
PM
0032-5155
1662-2758
General
10.4171/PM
http://www.ems-ph.org/doi/10.4171/PM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2008)
70
2013
3
Relations between minimal usco and minimal cusco maps
Ľubica
Holá
Academy of Sciences, BRATISLAVA, SLOVAK REPUBLIC
Dušan
Holý
Trnavská univerzita v Trnave, TRNAVA, SLOVAK REPUBLIC
Minimal cusco map, minimal usco map, quasicontinuous function, subcontinuous function, set-valued mapping, selection, extreme function
In our paper we give a characterization of (set-valued) maps which are minimal usco and minimal cusco simultaneously. Let $X$ be a topological space and $Y$ be a Banach space. We show that there is a bijection between the space $\operatorname{MU}(X,Y)$ of minimal usco maps from $X$ to $Y$ and the space $\operatorname{MC}(X,Y)$ of minimal cusco maps from $X$ to $Y$, and we study this bijection with respect to various topologies on underlying spaces. Let $X$ be a Baire space and $Y$ be a Banach space. Then $(\operatorname{MU}(X,Y),\tau_U)$ and $(\operatorname{MC}(X,Y),\tau_U)$ are homeomorphic, where $\tau_U$ is the topology of uniform convergence.
General topology
211
224
10.4171/PM/1931
http://www.ems-ph.org/doi/10.4171/PM/1931
Variational analysis for Dirichlet impulsive differential equations with oscillatory nonlinearity
Ghasem
Afrouzi
University of Mazandaran, BABOLSAR, IRAN
Armin
Hadjian
University of Mazandaran, BABOLSAR, IRAN
Vicenţiu
Rădulescu
University of Craiova, CRAIOVA, ROMANIA
Impulsive differential equations, Dirichlet condition, variational methods, infinitely many solutions
By using variational methods and critical point theory, we establish the existence of infinitely many solutions for second-order impulsive differential equations with Dirichlet boundary conditions, depending on two real parameters.
Ordinary differential equations
Manifolds and cell complexes
225
242
10.4171/PM/1932
http://www.ems-ph.org/doi/10.4171/PM/1932
Multiple points, scheme rank and symmetric tensor rank
Edoardo
Ballico
Università di Trento, TRENTO (TN), ITALY
Symmetric tensor rank, Veronese variety, scheme rank, multiple point, Waring decomposition
In this paper we prove some upper bounds for the symmetric tensor rank of a symmetric tensor (or a homogeneous polynomial) in terms of integers associated to any zero-dimensional scheme evincing the scheme rank of the homogeneous polynomial.
Algebraic geometry
Linear and multilinear algebra; matrix theory
243
250
10.4171/PM/1933
http://www.ems-ph.org/doi/10.4171/PM/1933
Warped product pointwise semi-slant submanifolds of Kähler manifolds
Bayram
Şahin
İnönü University, MALATYA, TURKEY
Warped product, pointwise slant submanifold, pointwise semi-slant submanifold, Kähler manifold
It is known that there exist no warped product semi-slant submanifolds in Kähler manifolds [15]. Recently, Chen and Garay studied pointwise slant submanifolds of almost Hermitian manifolds in [9] and obtained many new results for such submanifolds. In this paper, we first introduce pointwise semi-slant submanifolds of Kähler manifolds and then we show that there exists non-trivial warped product pointwise semi-slant submanifolds of Kähler manifold by giving an example, contrary to the semi-slant case. We present a characterization theorem and establish an inequality for the squared norm of the second fundamental form in terms of the warping function for such warped product submanifolds in Kähler manifolds. The equality case is also considered.
Differential geometry
251
268
10.4171/PM/1934
http://www.ems-ph.org/doi/10.4171/PM/1934
Rigidity index preservation of regular holonomic $\mathcal{D}$-modules under Fourier transform
Adelino
Paiva
Universidade de Lisboa, LISBOA, PORTUGAL
D-modules, Fourier transform, rigid local systems
This paper gives a purely algebraic proof that the Fourier transform preserves the rigidity index of irreducible regular holonomic $\mathcal{D}_{\mathbb{P}^1}[*\{\infty\}]$-modules.
Algebraic geometry
Number theory
269
293
10.4171/PM/1935
http://www.ems-ph.org/doi/10.4171/PM/1935