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Abstract polytopes are combinatorial structures obeying certain axioms that generalise both classical convex geometric polytopes (like the Platonic solids) and maps on surfaces (such as Klein's quartic). Every automorphism (symmetry) of an abstract polytope P is uniquely determined by its effect...
The paper deals with an extremal problem for bounded harmonic functions in the unit ball of R4. We solve the generalized Khavinson problem in R4. This precise problem was formulated by Kresin and Maz'ya for harmonic functions in the unit ball and in the half‐space of Rn. We find the optimal...
We show that the presence of one non‐degenerate, non‐contractible periodic orbit of a Hamiltonian on the standard symplectic torus implies the existence of infinitely many simple non‐contractible periodic orbits.
We prove that every finite non‐abelian simple group acts as the automorphism group of a chiral polyhedron, apart from the groups PSL2(q), PSL3(q), PSU3(q) and A7.
We investigate injective dimension of F‐finite F‐modules in characteristic p and holonomic D‐modules in characteristic 0. One of our main results is the following. If either
(a)R is a regular ring of finite type over an infinite field of characteristic p>0 and M is an FR‐finite FR‐module; or...
We study the Birman exact sequence for compact 3‐manifolds, obtaining a complete picture of the relationship between the mapping class group of the manifold and the mapping class group of the submanifold obtained by deleting an interior point. This covers both orientable manifolds and...
Two graphs G and H are hypomorphic if there exists a bijection φ:V(G)→V(H) such that G−v≅H−φ(v) for each v∈V(G). A graph G is reconstructible if H≅G for all H hypomorphic to G.
In this note, we prove that toric Kähler metrics on complex projective space, which are also U(n)‐invariant, are determined by their equivariant spectrum, that is, the list of eigenvalues of the Laplacian together with weights of the torus representation on the eigenspaces.
This note is about a type of quantitative density of closed geodesics on closed hyperbolic surfaces. The main results are upper bounds on the length of the shortest closed geodesic that ε‐fills the surface.
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