| 1. |
- Alvarado, Ryan, et al.
(författare)
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Sharp Geometric Maximum Principles for Semi-Elliptic Operators with Singular Drift
- 2011
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Ingår i: Mathematical Research Letters. - : International Press. - 1073-2780 .- 1945-001X. ; 18:4, s. 613-620
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Tidskriftsartikel (refereegranskat)abstract
- We discuss a sharp generalization of the Hopf-Oleinik boundary point principle (BPP) for domains satisfying an interior pseudo-ball condition, for non-divergence form, semi-elliptic operators with singular drift. In turn, this result is used to derive a version of the strong maximum principle under optimal pointwise blow-up conditions for the coefficients of the differential operator involved. We also explain how a uniform two-sided pseudo-ball condition may be used to provide a purely geometric characterization of Lyapunov domains, and clarify the role this class of domains plays vis-a-vis to the BPP.
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| 2. |
- Ammann, Bernd, et al.
(författare)
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Harmonic spinors and local deformations of the metric
- 2011
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Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 18:5, s. 927-936
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Tidskriftsartikel (refereegranskat)abstract
- Let (M, g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.
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| 3. |
- Benguria, Rafael D., et al.
(författare)
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The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space
- 2008
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Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 15:4, s. 613-622
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the upper half space H-3 subset of R-3 is given by the Sobolev constant. This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev type inequality whose sharp constant is determined as well.
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| 4. |
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| 5. |
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| 6. |
- Bouarroudj, Sofiane, et al.
(författare)
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Lie algebra deformations in characteristic 2
- 2015
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Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 22:2, s. 353-402
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Tidskriftsartikel (refereegranskat)abstract
- Of four types of Kaplansky algebras, type-2 and type-4 algebras have previously unobserved Z/2-gradings: nonlinear in roots. A method assigning a simple Lie superalgebra to every Z/2-graded simple Lie algebra in characteristic 2 is illustrated by seven new series. Type-2 algebras and one of the two type-4 algebras are demystified as nontrivial deforms (the results of deformations) of the alternate Hamiltonian algebras. The type-1 Kaplansky algebra is recognized as the derived of the nonalternate version of the Hamiltonian Lie algebra, the one that preserves a tensorial 2-form. Deforms corresponding to nontrivial cohomology classes can be isomorphic to the initial algebra, e.g., we confirm Grishkov's implicit claim and explicitly describe the Jurman algebra as such a semitrivial deform of the derived of the alternate Hamiltonian Lie algebra. This paper helps to sharpen the formulation of a conjecture describing all simple finite-dimensional Lie algebras over any algebraically closed field of nonzero characteristic and supports a conjecture of Dzhumadildaev and Kostrikin stating that all simple finite-dimensional modular Lie algebras are either of standard type or deforms thereof. In characteristic 2, we give sufficient conditions for the known deformations to be semitrivial.
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| 7. |
- Bridy, Andrew, et al.
(författare)
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Finite ramification for preimage fields of post-critically finite morphisms
- 2017
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Ingår i: Mathematical Research Letters. - : International Press of Boston, Inc.. - 1073-2780 .- 1945-001X. ; 24:6, s. 1633-1647
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Tidskriftsartikel (refereegranskat)abstract
- Given a finite endomorphism phi of a variety X defined over the field of fractions K of a Dedekind domain, we study the extension K (phi(-infinity)(alpha)) := boolean OR(n >= 1) K (phi(-n) (alpha)) generated by the preimages of alpha under all iterates of phi. In particular when phi is post-critically finite, i.e., there exists a non-empty, Zariski-open W subset of X such that phi(-1) (W) subset of W and phi : W -> X is etale, we prove that K (phi(-infinity) (alpha)) is rami fied over only finitely many primes of K. This provides a large supply of in finite extensions with restricted rami fication, and generalizes results of Aitken-Hajir-Maire [1] in the case X = A(1) and Cullinan-Hajir, Jones-Manes [7, 13] in the case X = P-1. Moreover, we conjecture that this finite rami fication condition characterizes post-critically finite morphisms, and we give an entirely new result showing this for X = P-1. The proof relies on Faltings' theorem and a local argument.
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| 8. |
- Burman, Yurii, et al.
(författare)
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Around matrix-tree theorem
- 2006
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Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 13:5--6, s. 761-774
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Tidskriftsartikel (refereegranskat)abstract
- Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the matrix-tree theorem for the root system Dn (the classical theorem corresponds to the An-case). Several byproducts of the developed technique, such as a new formula for a specialization of the multivariate Tutte polynomial, are of independent interest.
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| 9. |
- Costa, L., et al.
(författare)
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Derived category of fibrations
- 2011
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Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 18:3, s. 425-432
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we give a structure theorem for the derived category D(b)(X) of a Zariski locally trivial fibration X over Z with fiber F provided both F and Z have a full strongly exceptional collection of line bundles.
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| 10. |
- Coulembier, Kevin, et al.
(författare)
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Indecomposable manipulations with simple modules in category O
- 2019
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Ingår i: Mathematical Research Letters. - : INT PRESS BOSTON, INC. - 1073-2780 .- 1945-001X. ; 26:2, s. 447-499
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Tidskriftsartikel (refereegranskat)abstract
- We study the problem of indecomposability of translations of simple modules in the principal block of BGG category O for sl(n), as conjectured in [KiM1]. We describe some general techniques and prove a few general results which may be applied to study various special cases of this problem. We apply our results to verify indecomposability for n <= 6. We also study the problem of indecomposability of shufflings and twistings of simple modules and obtain some partial results.
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