Existence Theory of Minimal Hypersurfaces - Fernando Marquez
Explore the existence theory of minimal hypersurfaces, covering minimax theorems, space of cycles, and volume spectrum. Gain insights into Ricci curvature and generic metrics.
Optimal Transportation, Monge-Ampère Equations and Riemannian Ricci Bounds - Lecture 3
Explore geometric measure theory and optimal transport with a focus on Monge-Ampère equations and Riemannian Ricci bounds in this advanced mathematics lecture by L. Ambrosio.
Sharp Concavity of the Isoperimetric Profile Under Lower Ricci Bounds - Workshop on Synthetic Curvature Bounds
Explore sharp concavity of isoperimetric profiles in RCD spaces, extending Bavard-Pansu's work on Ricci curvature bounds to non-smooth, finite-dimensional settings.
Canonical Kaehler Metrics and Stability of Algebraic Varieties
Explore canonical Kähler metrics, algebraic variety stability, and the Yau-Tian-Donaldson conjecture in complex geometry. Delve into Kähler manifolds, curvature, and pluripotential theory with recent progress and applications.
Ricci Curvature and Functional Inequalities for Interacting Particle Systems
Explore entropic Ricci curvature bounds and their applications to interacting particle systems, focusing on functional inequalities and convergence rates to equilibrium in nonnegative curvature scenarios.
Curvature Bounds and the Length of the Shortest Closed Geodesic
Explore upper bounds for shortest periodic geodesics on Riemannian manifolds, examining curvature's impact on closed geodesic length in various geometric contexts.
Kähler Manifolds with Curvature Bounded Below
Explore Kähler manifolds with curvature bounded below, covering Yau's uniformization conjecture, compactification of manifolds, and Gromov-Hausdorff limits in this advanced mathematical survey.
Introduction to the Riemannian Curvature Dimension Condition - Lecture 3
Explore advanced concepts in Riemannian geometry with Prof. Gigli, focusing on the Curvature Dimension condition and its applications in non-smooth settings.
Introduction to the Riemannian Curvature Dimension Condition - Lecture 2
Explore advanced concepts in Riemannian geometry with Prof. Gigli, focusing on the Curvature Dimension condition and its applications in non-smooth settings.
Introduction to the Riemannian Curvature Dimension Condition - Lecture 1
Explore the Riemannian Curvature Dimension condition with Professor Nicola Gigli, delving into advanced mathematical concepts for graduate-level understanding of non-smooth geometry.
Tamed Spaces: Dirichlet Spaces with Distribution-Valued Ricci Bounds
Explore Dirichlet spaces with distribution-valued Ricci bounds, focusing on tamed spaces theory and singular perturbations of Dirichlet form. Investigate integrated Bochner inequality and Bakry-Émery condition generalizations.
Differentiating in a Non-Differentiable Environment
Explore differentiation in non-differentiable spaces, extending beyond traditional smooth manifolds to spaces with Ricci curvature bounds. Gain insights into advanced mathematical concepts.
A Lorentzian Analog for Hausdorff Dimension and Measure
Explore a novel approach to geometric dimension in Lorentzian spaces, comparing it to Hausdorff dimension and examining applications in spacetime analysis and synthetic curvature bounds.
Synthetic Time-like Ricci Curvature Lower Bounds: The Isoperimetric Inequality
Explore synthetic timelike Ricci curvature lower bounds and their implications for isoperimetric inequality in Lorentzian synthetic spaces.
Kato Meets Bakry-Émery: Curvature Conditions in Riemannian Geometry
Explore the relationship between Bakry-Émery curvature-dimension and Kato condition on Ricci curvature, uncovering insights on Kato limit spaces and Riemannian manifolds.
A Sharp Isoperimetric-Type Inequality for Lorentzian Spaces Satisfying Time-Like Ricci Curvature Lower Bounds
Explore sharp isoperimetric-type inequalities in Lorentzian spaces with time-like Ricci curvature bounds, including applications to black holes and cosmological space-times.
Unified Synthetic Ricci Curvature Lower Bounds for Riemannian and Sub-Riemannian Geometries
Explore unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian geometries through gauge metric measure spaces. Discover recent advances in metric measure and sub-Riemannian spaces.
Nonnegative Ricci Curvature, Nilpotency, and Hausdorff Dimension
Explore nonnegative Ricci curvature, nilpotency, and Hausdorff dimension in relation to universal covers, minimal representing loops, and asymptotic cones of manifolds.
Spaces with Ricci Curvature Lower Bounds
Explore recent findings on spaces with nonnegative Ricci curvature, including singular set dimensions, fractal-like Weyl's laws, and nonproper Busemann functions in manifolds.
Ricci Curvature, Fundamental Group and the Milnor Conjecture - Part 2
Explore advanced concepts in topology and geometry, focusing on counterexamples to the Milnor conjecture and their construction using mapping class groups and asymptotic cones.
Ricci Limit Spaces are Semi-Locally Simply Connected
Explore Ricci limit spaces and their semi-local simple connectivity, delving into fundamental groups and Gromov-Hausdorff convergence of Riemannian manifolds.