Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
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Explicit formulas for the Hodge-Laplacian spectrum on 1-forms of homogeneous 3-spheres are derived, and this spectrum determines the metric up to isometry.
An intrinsic effective sample size for manifold MCMC is defined via kernel discrepancy as the number of independent draws yielding equivalent expected squared discrepancy to the target.
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
The doubling conjecture holds for manifolds with boundary under a split-condition on fundamental groups of the inclusion, via surgery and minimal hypersurface methods.
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
The framework adds a deformation field P to a reference metric to define a total connection Gamma = ring Gamma + Lambda whose curvature, torsion, and nonmetricity are computed from the reference and deformation rather than postulated independently.
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Absolute continuity of generalized Wasserstein barycenters of finitely many measures
Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
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Hodge Laplacian on $1$-forms of homogeneous $3$-spheres
Explicit formulas for the Hodge-Laplacian spectrum on 1-forms of homogeneous 3-spheres are derived, and this spectrum determines the metric up to isometry.
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Intrinsic effective sample size for manifold-valued Markov chain Monte Carlo via kernel discrepancy
An intrinsic effective sample size for manifold MCMC is defined via kernel discrepancy as the number of independent draws yielding equivalent expected squared discrepancy to the target.
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Profile Likelihood Inference for Anisotropic Hyperbolic Wrapped Normal Models on Hyperbolic Space
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
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The doubling conjecture for positive scalar curvature
The doubling conjecture holds for manifolds with boundary under a split-condition on fundamental groups of the inclusion, via surgery and minimal hypersurface methods.
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Scale selection for geometric medians on product manifolds
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
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The Geometry of Dilation- and Shear-Deformed Spaces
The framework adds a deformation field P to a reference metric to define a total connection Gamma = ring Gamma + Lambda whose curvature, torsion, and nonmetricity are computed from the reference and deformation rather than postulated independently.