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Let M be a connected sum of complete Riemannian manifolds satisfying the volume doubling condition and the Poincaré inequality. We prove that the space of polynomial growth harmonic functions on M is finite dimensional whenever M has finitely many ends and satisfies the finite covering condition...
Let P be an abelian p-group, E a cyclic
-group acting freely on P and k an algebraically closed field of characteristic
. In this work, we prove that every self-equivalence of the stable module category of
comes from a self-equivalence of the derived category of...
Using a geometric approach, we define and investigate the conformal group of a symmetric space with twist. In the non-degenerate case we characterize this group by a theorem generalizing the fundamental theorem of projective geometry.
We study generic toric rings. We prove that they are Golod rings, so the Poincaré series of the residue field is rational. We classify when such a ring is Koszul, and compute its rate. Also resolutions related to the initial ideal of the toric ideal with respect to reverse lexicographic order...
In this paper, we first point out a relationship between the Second Main Theorem for algebriod functions in Nevanlinna theory and Wirsing's theorem in Diophantine approximation. This motivates a unified proof for both theorems. The second part of this paper deals with “moving targets” problem...
Let M be a module of finite length over a complete intersection (R,m) of characteristic
. We characterize the property that M has finite projective dimension in terms of the asymptotic behavior of a certain length function defined using the Frobenius functor. This may be viewed as the...
We consider the problem of the development of singularities for classical solutions to a new periodic shallow water equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution remains bounded but its slope becomes unbounded in finite time. A quite detailed description of the...
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