Markov convexity and local rigidity of distorted metrics

Abstract

It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type p if and only if it is Markov p-convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric spaces, showing in particular that tree metrics fail to have the dichotomy property.

47 pages, full version, replacing the previous version which was an announcement

Cited by in corpus (66)

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• The space of stability conditions on the local projective plane
• A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold
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• Projectivity and Birational Geometry of Bridgeland Moduli spaces on an Enriques Surface
• Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland's stability conditions
• Moment maps, nonlinear PDE, and stability in mirror symmetry
• Birational Geometry of Singular Moduli Spaces of O'Grady Type
• Counterexample to the Generalized Bogomolov-Gieseker Inequality for Threefolds
• Stability conditions on product threefolds of projective spaces and Abelian varieties
• Projectivity and Birational Geometry of Bridgeland moduli spaces
• Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
• The desingularization of the theta divisor of a cubic threefold as a moduli space
• Birational geometry of the intermediate Jacobian fibration of a cubic fourfold
• Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
• The Minimal Model Program for the Hilbert Scheme of Points on P^2 and Bridgeland Stability
• Some moduli spaces of Bridgeland's stability conditions
• Derived categories and the genus of space curves
• The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds
• Virtual counts on Quot schemes and the higher rank local DT/PT correspondence
• Stability conditions on threefolds with nef tangent bundles
• Scattering diagrams, stability conditions, and coherent sheaves on ${\mathbb{P}}^2$
• Nef cones of Hilbert schemes of points on surfaces
• A note on the Kuznetsov component of the Veronese double cone
• Some remarks on Fano threefolds of index two and stability conditions
• Mass growth of objects and categorical entropy
• Derived category of coherent sheaves and counting invariants
• Stability conditions and birational geometry of projective surfaces
• A classification of Lagrangian planes in holomorphic symplectic varieties
• Walls and asymptotics for Bridgeland stability conditions on 3-folds
• On pseudo-Anosov autoequivalences
• Serre-invariant stability conditions and Ulrich bundles on cubic threefolds
• T-structures on elliptic fibrations
• The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric Surface
• Bridgeland stability conditions on some threefolds of general type
• Bridgeland's stabilities on abelian surfaces
• Stability conditions on Calabi-Yau double/triple solids
• Stability and Applications
• Stability conditions on product varieties
• Families of elliptic curves in ${\mathbb{P}}^3$ and Bridgeland Stability
• Moduli of semistable sheaves as quiver moduli
• Fourier-Mukai transforms and stable sheaves on Weierstrass elliptic surfaces
• Stability conditions and extremal contractions
• Nef divisors for moduli spaces of complexes with compact support
• Some Quot schemes in tilted hearts and moduli spaces of stable pairs
• On the Bogomolov-Gieseker inequality in positive characteristic
• Weight functions, tilts, and stability conditions
• A note on Bogomolov-Gieseker type inequality for Calabi-Yau 3-folds
• A note on Bridgeland stability conditions and Catalan numbers
• A hyperbolic metric and stability conditions on K3 surfaces with ρ=1
• Stability conditions on morphisms in a category
• Characteristic classes and stability conditions for projective Kleinian orbisurfaces
• New moduli spaces of one-dimensional sheaves on ${\mathbb{P}}^3$
• Chern degree functions
• Stability and Fourier-Mukai Transforms on Higher Dimensional Elliptic Fibrations
• Stable pairs on local K3 surfaces
• Moduli spaces of sheaves on K3 surfaces
• Bridgeland stability conditions on normal surfaces
• Stable sheaves on bielliptic surfaces: from the classical to the modern
• The geometry of antisymplectic involutions, I
• Bayer-Macrì decomposition on Bridgeland moduli spaces over surfaces
• Stability conditions on affine Noetherian schemes
• Flops and Hilbert schemes of space curve singularities
• Zero Rank Asymptotic Bridgeland Stability
• On a deformation of gluing stability conditions
• Some quadratic inequalities on product varieties