In this paper, we introduce a method for resolving singularities of Galois closure covers for 5-fold covers between smooth surfaces. Applying this method, we determine types of singular fibers of a family of Galois closure curves for plane sextic curves. Consequently,we obtain an explicit construction of smooth projective minimal surfaces of general type with positive indices obtained as families of Galois closure curves of smooth plane sextic curves.
In this paper, we study the inverse mean curvature flow starting from a mean convex hypersurface in rank one symmetric spaces of non-compact type. We derive a lower bound for the mean curvature along the inverse mean curvature flow starting from a strictly star-shaped mean convex hypersurface.
In this paper, it is shown that if an extremal quasiconformal mapping f is of landslide type, then there exists another extremal quasiconformal mapping f~ in the Teichmüller equivalence class [f] such that the Beltrami differential of f~ is identical to a given Beltrami differential on the neighborhood of a landslide point. The key tool of the proof is the Reich-Strebel inequality.
This paper is concerned with the stability of a parallel flow of the compressible Navier-Stokes equation in a cylindrical domain. It is proved that the linearized semigroup around the parallel flow decays in the L2-norm as a one-dimensional heat semigroup when the Reynolds and Mach numbers are sufficiently small. The proof is given by combining the energy method of Iooss-Padula and a variant of the Matsumura-Nishida energy method.
We present a number of results about (finite) multiple harmonic sums modulo a prime, which provide interesting parallels to known results about multiple zeta values (i.e. infinite multiple harmonic series). In particular, we prove a ‘duality' result for mod p harmonic sums similar to (but distinct from) that for multiple zeta values. We also exploit the Hopf algebra structure of the quasi-symmetric functions to perform calculations with multiple harmonic sums mod p, and obtain, for each weight n through nine, a set of generators for the space of weight-n multiple harmonic sums mod p. When combined with recent work, the results of this paper offer significant evidence that the number of quantities needed to generate the weight-n multiple harmonic sums mod p is the nth Padovan number (OEIS sequence A000931).
Let K be a p-adic field and let E be an elliptic curve over K with potential good reduction. For some large Galois extension L of K containing all p-power roots of unity, we show the vanishing of certain Galois cohomology groups of L with values in the p-adic representation associated with E. We use these to prove analogous results in the global case. This generalizes some results of Coates, Sujatha and Wintenberger.
This paper defines mixed multiplicity systems; the Euler-Poincaré characteristic and the mixed multiplicity symbol of Nd-graded modules with respect to a mixed multiplicity system, and proves that the Euler-Poincaré characteristic and the mixed multiplicity symbol of any mixed multiplicity system of the type (k1,..., kd) and the (k1,..., kd)-difference of the Hilbert polynomial are the same. As an application, we obtain results for mixed multiplicities.
Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank K>1 is expansive. Bezuglyi et al (2009) extended the result to non-minimal cases. On the other hand, Gambaudo and Martens (2006) had expressed all Cantor minimal continuous surjections as the inverse limit of graph coverings. In this paper, we define a topological rank for every Cantor minimal continuous surjection, and show that every Cantor minimal continuous surjection of finite topological rank has the natural extension that is expansive.