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Saddle solutions for the fractional Choquard equation
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(−∆)u+ u = (Kα ∗ |u|)|u|u, x ∈ R where s ∈ (0, 1), N ≥ 3 and Kα is the Riesz potential with order α ∈ (0, N). For every Coxeter group G with rank 1 ≤ k ≤ N and p ∈ [2, N+α N−2s ), we construct a…
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In the spirit of Berestycki and Lions, we prove the existence of saddle type nodal solutions for the Choquard equation −∆u+ u = ( Iα ∗ F (u) ) F ′(u) in R where N ≥ 2 and Iα is the Riesz potential of…
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Coxter groups arose as a natural generalization of reflection groups. J. Tits defined them in a simple way using generators and relations, that is, using a group presentation W ∼= 〈S | R〉. Coxeter…
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We establish quasi-isometric rigidity for a class of right-angled Coxeter groups. Let $\Gamma_1,\Gamma_2$ be joins of finite generalized thick $m$-gons with $m\geq 3$. We show that the corresponding…
Automorphism Groups of Combinatorial Structures
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This is a series of lecture notes taken by students during a five lecture series presented by Anne Thomas in 2016 at the MATRIX workshop: The Winter of Disconnectedness.
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Buildings, volume 248 of Graduate Texts in Mathematics
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Reflection groups and Coxeter groups, volume 29 of Cambridge Studies in Advanced Mathematics
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Reflection Groups And Coxeter Groups
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The reflection groups and coxeter groups is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
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These notes are intended as an introduction to the theory of Coxeter groups. They closely follow my talk in the Lectures on Modern Mathematics Series at the Mathematical Sciences Center in Tsinghua…
The geometry and topology of Coxeter groups, volume 32 of London Mathematical Society Monographs Series
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W is finite then there is a point w ∈ W and a spherical subset T ⊆ S
We will need the following "Cartan-Hadamard Theorem for CAT(0) spaces" due to Gromov: Bibliography
The "conjugacy problem" for W is decidable. (This question still remains open for the "isomorphism problem
Σ is a finite-dimensional EW