Journal: Mathematische Zeitschrift

Abbreviation

Math. Z.

Publisher

Springer

Journal Volumes

ISSN

1432-1823
0025-5874

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Publications1 - 10 of 40
  • On the Upsilon invariant and satellite knots
    Item type: Journal Article
    Feller, Peter; Park, Junghwan; Ray, Arunima (2019)
    Mathematische Zeitschrift
  • Best constants in the exceptional case of Sobolev inequalities
    Item type: Journal Article
    Faget, Zoé (2006)
    Mathematische Zeitschrift
  • On the complement of the Richardson orbit
    Item type: Journal Article
    Baur, Karin; Hille, Lutz (2012)
    Mathematische Zeitschrift
  • The local-to-global property for Morse quasi-geodesics
    Item type: Journal Article
    Russell, Jacob; Spriano, Davide; Tran, Hung Cong (2022)
    Mathematische Zeitschrift
    We show the mapping class group, CAT(0) groups, the fundamental groups of closed 3-manifolds, and certain relatively hyperbolic groups have a local-to-global property for Morse quasi-geodesics. This allows us to generalize combination theorems of Gitik for quasiconvex subgroups of hyperbolic groups to the stable subgroups of these groups. In the case of the mapping class group, this gives combination theorems for convex cocompact subgroups. We show a number of additional consequences of this local-to-global property, including a Cartan-Hadamard type theorem for detecting hyperbolicity locally and discreteness of translation length of conjugacy classes of Morse elements with a fixed gauge. To prove the relatively hyperbolic case, we develop a theory of deep points for local quasi-geodesics in relatively hyperbolic spaces, extending work of Hruska.
  • On the existence of infinitely many invariant Reeb orbits
    Item type: Journal Article
    Merry, Will J.; Naef, Kathrin (2016)
    Mathematische Zeitschrift
  • The spectral decomposition of |θ|2
    Item type: Journal Article
    Nelson, Paul D. (2021)
    Mathematische Zeitschrift
    Let θ be an elementary theta function, such as the classical Jacobi theta function. We establish a spectral decomposition and surprisingly strong asymptotic formulas for ⟨|θ|2,φ⟩ as φ traverses a sequence of Hecke-translates of a nice enough fixed function. The subtlety is that typically |θ|2∉L2. Applications to the subconvexity, quantum variance and 4-norm problems are indicated.
  • Ruled Laguerre minimal surfaces
    Item type: Journal Article
    Skopenkov, Mikhail; Pottmann, Helmut; Grohs, Philipp (2012)
    Mathematische Zeitschrift
  • Arithmetic geometry of the moduli stack of Weierstrass fibrations over P1
    Item type: Journal Article
    Park, Jun-Yong; Schmitt, Johannes (2025)
    Mathematische Zeitschrift
    Coarse moduli spaces of Weierstrass fibrations over a smooth conic curve were constructed by the classical work of [Miranda] using geometric invariant theory. In our paper, we extend this treatment by using results of [Romagny] regarding group actions on stacks to give an explicit construction of the moduli stack Wn of Weierstrass fibrations over a smooth conic curve with discriminant degree 12n and a section. We show that it is a smooth algebraic stack and prove that for n≥2, the open substack Wmin,n of minimal Weierstrass fibrations is a separated Deligne–Mumford stack over any base field K with char(K)≠2,3 and ∤n. Arithmetically, for the moduli stack Wsf,n of stable Weierstrass fibrations, we determine its motive in the Grothendieck ring of stacks to be {Wsf,n}=L10n-2 in the case that n is odd, which results in its weighted point count to be #q(Wsf,n)=q10n-2 over Fq. In the appendix, we show how our methods can be applied similarly to the classical work of [Silverman] on coarse moduli spaces of self-maps of the projective line, allowing us to construct the natural moduli stack and to compute its motive.
  • Quantization for an elliptic equation of order 2m with critical exponential non-linearity
    Item type: Journal Article
    Martinazzi, Luca; Struwe, Michael (2012)
    Mathematische Zeitschrift
  • Asymptotic rank of spaces with bicombings
    Item type: Journal Article
    Descombes, Dominic (2016)
    Mathematische Zeitschrift
    The question, under what geometric assumptions on a space X an n-quasiflat in X implies the existence of an n-flat therein, has been investigated for a long time. It was settled in the affirmative for Busemann spaces by Kleiner, and for manifolds of non-positive curvature it dates back to Anderson and Schroeder. We generalize the theorem of Kleiner to spaces with bicombings. This structure is a weak notion of non-positive curvature, not requiring the space to be uniquely geodesic. Beside a metric differentiation argument, we employ an elegant barycenter construction due to Es-Sahib and Heinich by means of which we define a Riemannian integral serving us in a sort of convolution operation.
Publications1 - 10 of 40