Derives Clarke subdifferential and first-variation formula for the kth eigenvalue on self-adjoint operators (valid at essential spectrum edge) and applies it to characterize optimal weights in weighted Laplace/Steklov problems.
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Mazur and Jester manifolds have pairwise nonhomeomorphic boundaries via an octahedral hyperbolic structure, Dehn filling, and systolic geodesics, distinguishing their contractible 4-manifolds.
Closed-form expressions are derived for the expected hyperbolic volume of the convex hull of n beta-distributed random points in the d-dimensional unit ball under the Klein model.
CR Paneitz operator on non-embeddable 3D tori has infinitely many negative eigenvalues under mild assumptions.
Asymptotics are established for counting orbital points lying in one conjugacy class for cocompact and convex cocompact actions on negatively curved spaces.
citing papers explorer
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Eigenvalue optimization via a first-variation formula
Derives Clarke subdifferential and first-variation formula for the kth eigenvalue on self-adjoint operators (valid at essential spectrum edge) and applies it to characterize optimal weights in weighted Laplace/Steklov problems.
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Mazur's knot and the Octahedron
Mazur and Jester manifolds have pairwise nonhomeomorphic boundaries via an octahedral hyperbolic structure, Dehn filling, and systolic geodesics, distinguishing their contractible 4-manifolds.
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Expected hyperbolic volumes of random beta polytopes
Closed-form expressions are derived for the expected hyperbolic volume of the convex hull of n beta-distributed random points in the d-dimensional unit ball under the Klein model.
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Non-embeddable torus and CR Paneitz operator
CR Paneitz operator on non-embeddable 3D tori has infinitely many negative eigenvalues under mild assumptions.
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Orbital Counting in Conjugacy Classes
Asymptotics are established for counting orbital points lying in one conjugacy class for cocompact and convex cocompact actions on negatively curved spaces.