Polynomially Convex Embeddings of Real Manifolds in C^n
Explore geometric embeddings of real manifolds in complex spaces, focusing on polynomial convexity and its connections to approximation theory and diverse mathematical areas.
Nash's C^1 Isometric Embedding Theorem and the Borisov-Gromov Problem - Lecture 3
Explore Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem in Riemannian geometry. Delve into surprising constructions and open questions linked to the Onsager conjecture.
On Weak 1-Semiconvexity of Open Sets in Euclidean Spaces
Explore weak 1-semiconvexity in Euclidean spaces, examining its properties, connections to linearly accessible domains, and implications for set disconnectedness in higher dimensions.
Sobolev Spaces: Density of Test Functions in Euclidean Space - Part 2
Explore density of test functions in Sobolev spaces on Euclidean space, advancing understanding of mathematical analysis.
Recent Developments in Constant Mean Curvature Hypersurfaces - Part II
Explore recent developments in constant mean curvature hypersurfaces, focusing on min-max theorems and the half-volume spectrum. Gain insights into advanced geometric analysis concepts.
Intrinsic Flat Stability of the Positive Mass Theorem for Graphical Manifolds
Explore intrinsic flat stability of positive mass theorem for graphical manifolds, focusing on asymptotically flat and hyperbolic cases. Gain insights into rigidity, stability, and ongoing research.
Geometric Inequalities Between Intrinsic and Extrinsic Curvature Invariants
Explore geometric inequalities between intrinsic and extrinsic curvature invariants in Riemannian manifolds, focusing on Nash's Theorem and recent developments in the field.
Sticky Kakeya Sets and the Sticky Kakeya Conjecture
Explore the intriguing world of Kakeya sets and delve into the sticky Kakeya conjecture. Uncover groundbreaking insights on this fundamental problem in harmonic analysis and Fourier transform behavior.
Complexity of Submanifolds and Colding-Minicozzi Entropy
Explore Colding-Minicozzi entropy's role in analyzing submanifold complexity and its applications to mean curvature flow singularities and hypersurface simplicity.
Finite Point Configurations in Euclidean, Discrete, and Arithmetic Settings
Explore finite point configurations across Euclidean, discrete, and arithmetic spaces. Discover size requirements for subsets containing congruent copies of given configurations, with connections to learning theory.
Minimal Surfaces and the Isoperimetric Inequality
Explore the generalization of the isoperimetric inequality to submanifolds in Euclidean space, focusing on minimal submanifolds and their sharp isoperimetric properties.
Hausdorff Dimension of Three-Dimensional Kakeya Sets
Explore groundbreaking research on Kakeya sets in R^3, uncovering a new lower bound for Hausdorff dimension and its implications in geometric measure theory.
Large Steklov Eigenvalues Under Geometric Constraints
Explore large Steklov eigenvalues in compact Riemannian manifolds, examining geometric constraints and constructing metrics with fixed volume and boundary conditions.
Hausdorff Dimension of Three-Dimensional Kakeya Sets
Explore groundbreaking research on Kakeya sets in R^3, uncovering a new lower bound for Hausdorff dimension and its implications in geometric measure theory.
Generic Dynamics of the Mean Curvature Flows
Explore generic dynamics of mean curvature flows, including perturbation of shrinkers and isolatedness of cylindrical singularities in hypersurface evolution.
Optimal Immersions in the Calculus of Variations of Surfaces
Explore innovative minmax techniques for optimal surface immersions, including recent progress on Yau, Willmore, and 16π conjectures in calculus of variations.
Capacity in Low Regularity with Connections to General Relativity
Explore capacity in metric spaces, its behavior under convergence, and connections to general relativity's total mass concept.
On the Uniqueness Problem for Spacetime Extensions
Explore uniqueness conditions for Lorentzian manifold extensions, analyzing boundary agreement and presenting recent findings on necessary conditions and non-uniqueness mechanisms.
The Brownian Transport Map - IPAM at UCLA
Explore Lipschitz transport maps between probability measures, focusing on the Brownian transport map's construction, properties, and applications to Euclidean functional inequalities.
Skeletonization Algorithms With Theoretical Guarantees for Point Clouds
Explore skeletonization algorithms for point clouds, including Mapper, alpha-Reeb graphs, and Homologically Persistent Skeleton. Compare their performance on synthetic and real data sets.
Sphere Packings with Forbidden Distances
Delve into the mathematical exploration of sphere packing configurations, examining forbidden distances and their implications in geometric number theory through advanced analytical approaches.