Horizontal gradient of polynomials

DOI10.5802/aif.2481zbMath1197.14058OpenAlexW4300381888MaRDI QIDQ1041271

Krzysztof Kurdyka, Si Tiep Dinh, Patrice Orro

Publication date: 2 December 2009

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/10445

zbMATH Keywords

sub-Riemannian metricsemi-algebraicLojasiewicz inequality

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Sub-Riemannian geometry (53C17) Vector distributions (subbundles of the tangent bundles) (58A30)

Related Items

Gradient trajectories for plane singular metrics. I: Oscillating trajectories ⋮ Horizontal gradient of polynomial functions for the standard Engel structure on \(\mathbb R^4\)

Cites Work

• Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
• Problèmes rencontrés dans mon parcours mathématique: Un bilan. (Problems I have come across during my mathematical career: A balance)
• Sub-Riemannian geometry
• Semianalytic and subanalytic sets
• Singularity theory and an introduction to catastrophe theory
• On gradients of functions definable in o-minimal structures
• On semi- and subanalytic geometry
• A gradient flow approach to decentralised output feedback optimal control
• On the Łojasiewicz--Simon gradient inequality.
• Convergence properties of gradient descent noise reduction
• The multimode Procrustes problem
• Multiplicities of Pfaffian intersections, and the Łojasiewicz inequality
• Singular solutions, homogeneous norms, and quasiconformal mappings in Carnot groups
• A blow-up theorem for regular hypersurfaces on nilpotent groups
• A dual purpose principal and minor component flow
• On the stable equilibrium points of gradient systems
• Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung
• BOUNDS FOR GRADIENT TRAJECTORIES AND GEODESIC DIAMETER OF REAL ALGEBRAIC SETS
• Differential Topology
• A gradient flow approach to computing lq optimal output feedback gains
• Orbits of Families of Vector Fields and Integrability of Distributions
• Explicit bounds for the Łojasiewicz exponent in the gradient inequality for polynomials
• Proof of the gradient conjecture of R. Thom.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item