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  • 1.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F.
    UNED, Spain .
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    ON THE CONNECTIVITY OF BRANCH LOCI OF MODULI SPACES2013In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, no 1, p. 245-258Article in journal (Refereed)
    Abstract [en]

    The moduli space M-g of compact Riemann surfaces of genus g has orbifold structure and the set of singular points of the orbifold is the branch locus B-g. In this article we show that B-g is connected for genera three, four, thirteen, seventeen, nineteen and fiftynine, and disconnected for any other genus. In order to prove this we use Fuchsian groups, automorphisms of order 5 and 7 of Riemann surfaces, and calculations with GAP for some small genera.

  • 2.
    Björn, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Removable singularities for bounded p-harmonic and quasi(super)harmonic functions2006In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 31, p. 71-95Article in journal (Refereed)
  • 3.
    Björn, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Removable singularities for H-p spaces of analytic functions, 0 < p < 12001In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 26, no 1, p. 155-174Article in journal (Refereed)
    Abstract [en]

    In this paper we study removable singularities for Hardy H-p spaces of analytic functions on general domains, mainly for 0 < p < 1. For each p < 1 we prove that there is a self-similar linear Canter set with Hausdorff dimension greater than 0.4p removable for H-p, thereby obtaining the first removable sets with positive Hausdorff dimension for 0 < p < 1. (Cf. the author's older result that a set E removable for H-P, 0 < p < 1, must satisfy dim E p.) We use this to extend some results earlier proved for 1 less than or equal to p < to 0 < p < infinity or 1/2 less than or equal to p < .

  • 4.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Latvala, Visa
    University of Eastern Finland, Finland.
    SOBOLEV SPACES, FINE GRADIENTS AND QUASICONTINUITY ON QUASIOPEN SETS2016In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 41, no 2, p. 551-560Article in journal (Refereed)
    Abstract [en]

    We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space X equipped with a doubling measure supporting a p-Poincare inequality with 1 amp;lt; p amp;lt; infinity, and connect them to the Sobolev theory in R-n. In particular, we show that for quasiopen subsets of R-n the Newtonian functions, which are naturally defined in any metric space, coincide with the quasicontinuous representatives of the Sobolev functions studied by Kilpelainen and Maly in 1992.

  • 5.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Mirumbe, Ismail
    Makerere Univ, Uganda.
    THE QUASISUPERMINIMIZING CONSTANT FOR THE MINIMUM OF TWO QUASISUPERMINIMIZERS IN R-n2020In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 45, p. 215-225Article in journal (Refereed)
    Abstract [en]

    It was shown in Bjorn-Bjorn-Korte [5] that u := min{u(1), u(2)} is a (Q) over bar -quasisuper-minimizer if u(1) and u(2) are Q-quasisuperminimizers and (Q) over bar = 2Q(2)/(Q+1). Moreover, one-dimensional examples therein show that (Q) over bar is close to optimal. In this paper we give similar examples in higher dimensions. The case when u(1) and u(2) have different quasisuperminimizing constants is considered as well.

  • 6.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Poincare inequalities for powers and products of admissible weights2001In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 26, no 1, p. 175-188Article in journal (Refereed)
    Abstract [en]

    Our main result is that if mu is an s-admissible measure in R-n and nu is an element of A(p)(d mu), then the measure d nu = nu d mu is ps-admissible. A two-weighted version of this result is also proved. It is further shown that every strong A(infinity) -weight omega in R-n, n greater than or equal to 2, is n/(n - 1)-admissible, that its power omega (1-1/n) is 1-admissible and that the weights W1-p/n With 1 < p < n are q-admissible for some q < p. A counterexample showing that we cannot take q = 1 in general is also given. Finally, a new class of p-admissible weights is described.

  • 7.
    Costa, AF
    et al.
    Univ Nacl Educ Distancia, Fac Ciencias, Dept Matemat Fundamentales, E-28040 Madrid, Spain Linkoping Univ, Inst Matemat, S-58183 Linkoping, Sweden.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On the connectedness of the locus of real Riemann surfaces2002In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 27, no 2, p. 341-356Article in journal (Refereed)
    Abstract [en]

    It is well known that the functorial equivalence between pairs (X, sigma), where X is a Riemann surface which admits an antiholomorphic involution (symmetry) sigma: X --> X, and real algebraic curves. We shall refer to such Riemann surfaces as real Riemann surfaces, following Klein's terminology. We consider the sets M-g(R) and M-g(2R) of real curves and :real hyperelliptic curves, respectively in the moduli space M-g of complex algebraic curves of genus g. In this paper we prove that any real hyperelliptic Riemann surface can be quasiconformally deformed, preserving the real and hyperelliptic character, to a real hyperelliptic Riemann surface (X, sigma), such that X admits a symmetry tau, where Fix (tau) is connected and non-separating. As a consequence, we obtain the connectedness of the sets M-g(2R)(subset of M-g) of all real hyperelliptic Riemann surfaces of genus g and M-g(R)(subset of M-g) of all real Riemann surfaces of given genus g using a procedure different from the one given by Seppala for M-g(2R) and Buser, Seppala and Silhol for M-g(R). A Riemann surface X is called a p-gonal Riemann surface, where p is a prime, if there exists a p-fold covering map from X onto the Riemann sphere. We prove ill this paper that the subset of real p-gonal Riemann surfaces, p greater than or equal to 3, is not a connected subset of M-g in general. This generalizes a result of Gross and Harris for real trigonal algebraic curves.

  • 8.
    Farnana, Zohra
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    The double obstacle problem on metric spaces2009In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 34, no 1, p. 261-277Article in journal (Refereed)
    Abstract [en]

    We study the double obstacle problem on a metric measure space equipped with a doubling measure. and supporting a p-Poincare inequality. We prove existence and uniqueness. We also prove the continuity of the solution of the double obstacle. problem with continuous obstacles and show that. the continuous solution is a minimizer in the open set where it. does not touch the two obstacles. Moreover we consider the regular boundary points and show that the solution of the double obstacle problem on a regular open set with continuous obstacles is continuous up to the boundary. Regularity of boundary points is further characterized in some other ways using the solution of the double obstacle problem.

  • 9.
    Hansevi, Daniel
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in Rn and metric spaces2015In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 40, p. 89-108Article in journal (Refereed)
    Abstract [en]

    The obstacle problem associated with p-harmonic functions is extended to unbounded open sets, whose complement has positive capacity, in the setting of a proper metric measure space supporting a (p,p)-Poincaré inequality, 1<p<∞, and the existence of a unique solution is proved. Furthermore, if the measure is doubling, then it is shown that a continuous obstacle implies that the solution is continuous, and moreover p-harmonic in the set where it does not touch the obstacle. This includes, as a special case, the solution of the Dirichlet problem for p-harmonic functions with Sobolev type boundary data.

  • 10.
    Hidalgo, Ruben A.
    et al.
    University of Tecn Federico Santa Maria, Chile .
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    ON THE CONNECTIVITY OF THE BRANCH LOCUS OF THE SCHOTTKY SPACE2014In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 39, no 2, p. 635-654Article in journal (Refereed)
    Abstract [en]

    Let M be a handlebody of genus g greater than= 2. The space T(M), that parametrizes marked Kleinian structures on M up to isomorphisms, can be identified with the space MSg, of marked Schottky groups of rank g, so it carries a structure of complex manifold of finite dimension 3(g - 1). The space M(M) parametrizing Kleinian structures on M up to isomorphisms, can be identified with S-g, the Schottky space of rank g, and it carries the structure of a complex orbifold. In these identifications, the projection map pi: T(M) -greater than M(M) corresponds to the map from MSg, onto S-g that forgets the marking. In this paper we observe that the singular locus B(M) of M(M), that is, the branch locus of pi, has (i) exactly two connected components for g = 2, (ii) at most two connected components for g greater than= 4 even, and (iii) M(M) is connected for g greater than= 3 odd.

  • 11.
    Malý, Lukáš
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices2013In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, no 2, p. 727-745Article in journal (Refereed)
    Abstract [en]

    Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of particular interest. Existence of minimal weak upper gradients in this general setting is proven and corresponding representation formulae are given. Furthermore, the connection between pointwise convergence of a sequence of Newtonian functions and its convergence in norm is studied.

  • 12.
    Svensson, Olof
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology, Communications and Transport Systems.
    Di Biase, Fausto
    Dipartimento di Scienze Universita G. dAnnunzio.
    Stokolos, Alexander
    Department of Mathematics DePaul University.
    Weiss, Tomasz
    Institute of Mathematics Akademia Podlaska.
    On the sharpness of the Stolz approach2006In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 31, no 1, p. 47-59Article in journal (Refereed)
    Abstract [en]

    We study the sharpness of the Stolz approach for the a.e. convergence of functions in the Hardy spaces in the unit disc, first settled in the rotation invariant case by J. E. Littlewood in 1927 and later examined, under less stringent, quantitative hypothesis, by H. Aikawa in 1991. We introduce a new regularity condition, of a qualitative type, under which we prove a version of Littlewood's theorem for tangential approach whose shape may vary from point to point. Our regularity condition can be extended in those contexts where no group is involved, such as NTA domains in Rn. We show exactly in what sense our regularity condition is sharp.

1 - 12 of 12
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