On the Morse-Bott property of analytic functions on Banach spaces with Łojasiewicz exponent one half

DOI10.1007/s00526-020-01734-4zbMath1444.32029arXiv1803.11319OpenAlexW3098261052MaRDI QIDQ1988501

Paul M. N. Feehan

Publication date: 23 April 2020

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.11319

zbMATH Keywords

analytic functioncritical pointBanach spaceMorse-Bott functionŁojasiewicz gradient inequality

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Real-analytic and semi-analytic sets (14P15) Local complex singularities (32S05)

Related Items (2)

Łojasiewicz-Simon gradient inequalities for analytic and Morse-Bott functions on Banach spaces ⋮ Optimal Łojasiewicz-Simon inequalities and Morse-Bott Yang-Mills energy functions

Cites Work

• Variational Methods
• Positively homogeneous functions and the Łojasiewicz gradient inequality
• MINIMAL SUBMANIFOLDS
• On the Volume Elements on a Manifold
• Analytic Functions in Banach Spaces
• Symplectic structures on Banach manifolds
• The Morse lemma for Banach spaces
• Morse theory on Banach manifolds
• The Morse Lemma on Banach Spaces
• Dynamics in One Complex Variable. (AM-160)
• An invitation to Morse theory
• The deformation theory of representations of fundamental groups of compact Kähler manifolds
• Riemannian geometry and geometric analysis
• Dynamics of evolutionary equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol'd
• The dimension and structure of the space of harmonic 2-spheres in the \(m\)-sphere
• Notes on the extension of the mean curvature flow
• The Łojasiewicz gradient inequality in the infinite-dimensional Hilbert space framework
• Lecture notes on mean curvature flow
• Mean curvature flow of pinched submanifolds to spheres
• Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
• Jacobi fields along harmonic 2-spheres in 3- and 4-spheres are not all integrable
• The analysis of linear partial differential operators. III: Pseudo-differential operators
• Mean curvature flow and isoperimetric inequalities. Edited by Vicente Miquel and Joan Porti
• Functional analysis, Sobolev spaces and partial differential equations
• Semigroups of linear operators and applications to partial differential equations
• Deforming metrics in the direction of their Ricci tensors
• On the Jacobi differential operators associated to minimal isometric immersions of symmetric spaces into spheres. II
• On the Jacobi differential operators associated to minimal isometric immersions of symmetric spaces into spheres. III
• Semianalytic and subanalytic sets
• On the radial behavior of minimal surfaces and the uniqueness of their tangent cones
• Geometric theory of semilinear parabolic equations
• On the Jacobi differential operators associated to minimal isometric immersions of symmetric spaces into spheres. I
• Manifolds, tensor analysis, and applications.
• Higgs bundles and local systems
• The manifold structure of maps between open manifolds
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
• Rigidity in the harmonic map heat flow
• A long exact sequence for symplectic Floer cohomology
• On the Łojasiewicz--Simon gradient inequality.
• Regularity theory for mean curvature flow
• Introduction to differentiable manifolds.
• Bifurcation theory of functional differential equations
• Optimal Łojasiewicz-Simon inequalities and Morse-Bott Yang-Mills energy functions
• Łojasiewicz-Simon gradient inequalities for analytic and Morse-Bott functions on Banach spaces
• Resolution of singularities and geometric proofs of the Łojasiewicz inequalities
• Resolution of singularities of an algebraic variety over a field of characteristic zero. II
• Uniformly compressing mean curvature flow
• Slowly converging Yamabe flows
• Uniqueness of blowups and Łojasiewicz inequalities
• The gradient structure of the mean curvature flow
• Rigidity of the harmonic map heat flow from the sphere to compact Kähler manifolds
• The stable homotopy of the classical groups
• Morse theory and a non-linear generalization of the Dirichlet problem
• The Banach manifold $C^{k}(M,N)$
• Submanifold theory. Beyond an introduction
• Geometry of manifolds of maps
• Minimal varieties in Riemannian manifolds
• On the complemented subspaces problem
• On differentiable functions with isolated critical points
• A proof of the Morse-Bott lemma.
• Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
• Morse theory on Hilbert manifolds
• Nondegenerate critical manifolds
• Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations
• Mean Curvature Flow in Higher Codimension: Introduction and Survey
• Lojasiewicz inequalities and applications
• A Representation Theorem for Differentiable Functions
• Jacobi Fields Along Harmonic 2-Spheres in CP ² are Integrable
• A Note on the Topological Degree at a Critical Point of Mountainpass-Type
• Minimal Surfaces
• Abstract Parabolic Evolution Equations and their Applications
• On the Yang-Mills heat equation in two and three dimensions.
• The Second Variation Formula for Harmonic Mappings
• On the Volume Decreasing Property of a Class of Real Harmonic Mappings
• Harmonic Mappings of Spheres
• Elliptic regularization and partial regularity for motion by mean curvature
• The Space of Harmonic Maps from the 2-Sphere to the Complex Projective Plane
• The Morse-Palais lemma on Banach spaces
• Introduction to Global Analysis
• Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions
• Shorter Notes: An Elementary Proof of the Morse-Palais Lemma for Banach Spaces
• Mean curvature flow
• On the bumpy metrics theorem for minimal submanifolds

This page was built for publication: On the Morse-Bott property of analytic functions on Banach spaces with Łojasiewicz exponent one half