Evolution of form and shape
From MaRDI portal
Publication:6118169
DOI10.4171/icm2022/142OpenAlexW4389775764MaRDI QIDQ6118169
Publication date: 20 March 2024
Published in: International Congress of Mathematicians (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4171/icm2022/142
minimal surfacesgeometric flowsarrival timefunction theory on manifoldsuniqueness of blowupsdegenerate elliptic and parabolic PDEsoptimal regularity and growth
Nonlinear parabolic equations (35K55) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Second-order elliptic equations (35J15) Ricci flows (53E20)
Cites Work
- Embedded self-similar shrinkers of genus 0
- The singular set of mean curvature flow with generic singularities
- On \(\kappa\)-noncollapsed complete noncompact shrinking gradient Ricci solitons which split at infinity
- Three-circle theorem and dimension estimate for holomorphic functions on Kähler manifolds
- Self-shrinkers for the mean curvature flow in arbitrary codimension
- The round sphere minimizes entropy among closed self-shrinkers
- Generic mean curvature flow. I: Generic singularities
- Smooth compactness of self-shrinkers
- Noncollapsing in mean-convex mean curvature flow
- The space of embedded minimal surfaces of fixed genus in a 3-manifold. V. Fixed genus
- \(\mathcal{F}\)-stability for self-shrinking solutions to mean curvature flow
- Structure theory of singular spaces
- A topological property of asymptotically conical self-shrinkers of small entropy
- Non-properly embedded \(H\)-planes in \(\mathbb{H}^3\)
- A finitary version of Gromov's polynomial growth theorem.
- On complete gradient shrinking Ricci solitons
- Topology and curvature of minimal surfaces properly embedded in \(\mathbb{R}^ 3\)
- Calabi-Yau manifolds with isolated conical singularities
- The strong halfspace theorem for minimal surfaces
- Flow by mean curvature of convex surfaces into spheres
- Stable minimal surfaces in Euclidean space
- The Dirichlet problem at infinity for manifolds of negative curvature
- The Dirichlet problem at infinity for a negatively curved manifold
- Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
- Motion of level sets by mean curvature. I
- A local regularity theorem for mean curvature flow
- Complexity of parabolic systems
- Strong uniqueness of the Ricci flow
- Universality in mean curvature flow neckpinches
- Linear stability of Perelman's \(\nu\)-entropy on symmetric spaces of compact type
- Asymptotic behavior for singularities of the mean curvature flow
- Sharp logarithmic Sobolev inequalities on gradient solitons and applications
- On a classification of gradient shrinking solitons
- Notes on Perelman's papers
- Mean curvature flow with surgeries of two-convex hypersurfaces
- Positive harmonic functions on complete manifolds of negative curvature
- On the parabolic kernel of the Schrödinger operator
- The heat equation shrinking convex plane curves
- Nonlinear analysis in geometry
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- The heat equation shrinks embedded plane curves to round points
- Linear growth harmonic functions on a complete manifold
- Level set approach to mean curvature flow in arbitrary codimension
- Spaces with Ricci curvature bounds
- On the radial behavior of minimal surfaces and the uniqueness of their tangent cones
- A complete minimal surface in \(R^ 3\) between two parallel planes
- Topology of three dimensional manifolds and the embedding problems in minimal surface theory
- Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
- Nodal domains and growth of harmonic functions on noncompact manifolds
- Curvature estimates for minimal hypersurfaces
- Harmonic functions on manifolds
- Inhomogeneous Einstein metrics on low-dimensional spheres and other low-dimensional spaces
- Mean curvature flow singularities for mean convex surfaces
- Ricci solitons on compact three-manifolds
- On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay
- Harmonic functions with polynomial growth
- Weyl type bounds for harmonic functions
- Some geometric properties of the Bakry-Émery-Ricci tensor
- Convexity estimates for mean curvature flow and singularities of mean convex surfaces
- The space of cycles, a Weyl law for minimal hypersurfaces and Morse index estimates
- Entropy of closed surfaces and min-max theory
- Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure
- Singular Ricci flows. I
- Unique asymptotics of ancient convex mean curvature flow solutions
- The space of embedded minimal surfaces of fixed genus in a 3-manifold. I: Estimates off the axis for disks
- The space of embedded minimal surfaces of fixed genus in a 3-manifold. II: Multi-valued graphs in disks
- The space of embedded minimal surfaces of fixed genus in a 3-manifold. III: Planar domains
- The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV: Locally simply connected
- Sharp frequency bounds for eigenfunctions of the Ornstein-Uhlenbeck operator
- Three-manifolds with positive Ricci curvature
- Complete properly embedded minimal surfaces in \(\mathbf R^3\)
- Harmonic functions of linear growth on Kähler manifolds with nonnegative Ricci curvature
- Mean curvature flow through singularities for surfaces of rotation
- Harmonic functions of polynomial growth on complete manifolds. II
- Linear growth harmonic functions on complete manifolds with nonnegative Ricci curvature
- Lower bounds on Ricci curvature and the almost rigidity of warped products
- New monotonicity formulas for Ricci curvature and applications. I
- Weighted \(L^2\) version of Mergelyan and Carleman approximation
- Limit lamination theorem for H-disks
- The embedded Calabi-Yau conjecture for finite genus
- Uniqueness of asymptotically conical tangent flows
- Wandering singularities
- Optimal bounds for ancient caloric functions
- Uniqueness and stability of Ricci flow through singularities
- Ancient low-entropy flows, mean-convex neighborhoods, and uniqueness
- Uniqueness of two-convex closed ancient solutions to the mean curvature flow
- Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
- Dynamics of closed singularities
- The singular structure and regularity of stationary varifolds
- On uniqueness of tangent cones for Einstein manifolds
- Properly embedded minimal planar domains
- Rigidity and stability of Einstein metrics for quadratic curvature functionals
- Rigidity of gradient Ricci solitons
- On the entropy of closed hypersurfaces and singular self-shrinkers
- Liouville properties
- Rigidity of asymptotically conical shrinking gradient Ricci solitons
- Uniqueness of blowups and Łojasiewicz inequalities
- Rigidity of generic singularities of mean curvature flow
- Mean curvature flow with surgery
- The uniqueness of the helicoid
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The singular set of 1-1 integral currents
- Existence of infinitely many minimal hypersurfaces in positive Ricci curvature
- Uniqueness of convex ancient solutions to mean curvature flow in \({\mathbb {R}}^3\)
- The Calabi-Yau conjectures for embedded surfaces
- Rotational symmetry of self-similar solutions to the Ricci flow
- Ricci curvature and monotonicity for harmonic functions
- Uniqueness of compact tangent flows in mean curvature flow
- Rotational symmetry of Ricci solitons in higher dimensions
- A sharp lower bound for the entropy of closed hypersurfaces up to dimension six
- Existence of infinitely many minimal hypersurfaces in closed manifolds
- An overview of periodic elliptic operators
- Differentiability of the Arrival Time
- New Logarithmic Sobolev Inequalities and an ɛ-Regularity Theorem for the Ricci Flow
- Lojasiewicz inequalities and applications
- Level Set Method for Motion by Mean Curvature
- Mean Curvature Flow of Mean Convex Hypersurfaces
- Eigenvalues of the drifted Laplacian on complete metric measure spaces
- Uniqueness of self-similar shrinkers with asymptotically conical ends
- Recent Progress on Ricci Solitons
- A new proof of Gromov’s theorem on groups of polynomial growth
- Seminar On Minimal Submanifolds. (AM-103)
- The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
- Harmonic functions on complete riemannian manifolds
- Differential equations on riemannian manifolds and their geometric applications
- The Motion of a Surface by Its Mean Curvature. (MN-20)
- Singularities of harmonic maps
- Stratification of minimal surfaces, mean curvature flows, and harmonic maps.
- Large scale behavior of kernels of Schrodinger operators
- Liouville theorems for harmonic sections and applications
- Regularity of the Level Set Flow
- The nature of singularities in mean curvature flow of mean-convex sets
- A monotonicity formula on complete Kähler manifolds with nonnegative bisectional curvature
- Eigenvalue Comparison on Bakry-Emery Manifolds
- The size of the singular set in mean curvature flow of mean-convex sets
- Extrinsic Geometric Flows
- Recent Developments in Ricci Flows
- Asymptotic structure of almost eigenfunctions of drift Laplacians on conical ends
- Helicoid-like minimal disks and uniqueness
- In Search of Stable Geometric Structures
- Arnold‐Thom Gradient Conjecture for the Arrival Time
- Regularity and compactness for stable codimension $1$ CMC varifolds
- On Ancient Solutions of the Heat Equation
- Mean curvature flow
- Uniqueness of Tangent Cones for Two‐Dimensional Almost‐Minimizing Currents
- A New Golden Age of Minimal Surfaces
- NEW COMPLEX ANALYTIC METHODS IN THE THEORY OF MINIMAL SURFACES: A SURVEY
- Shapes of embedded minimal surfaces
- Rate of convergence of the mean curvature flow
- A deterministic‐control‐based approach motion by curvature
- The stability of self-shrinkers of mean curvature flow in higher co-dimension
- The geometry of $G$-structures
- Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
- Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces
- Mean curvature flow with surgery of mean convex surfaces in \(\mathbb R^3\)