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.
Failure of the Curvature-Dimension Condition in Sub-Finsler Manifolds
Explore the failure of curvature-dimension conditions in sub-Finsler manifolds, focusing on recent proofs and implications for sub-Riemannian geometry and the Heisenberg group.
Sobolev Spaces in Extended Metric-Topological Measure Spaces
Explore Sobolev spaces in extended metric-topological measure spaces, focusing on Cheeger energy construction and properties in this general framework.
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.
Dimension-Independent Functional Inequalities on Sub-Riemannian Manifolds
Explore gradient estimates and functional inequalities on sub-Riemannian manifolds, focusing on techniques like tensorisation and quotients for spaces without curvature bounds.
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.
Rigidity of Mass-Preserving 1-Lipschitz Maps from Integral Current Spaces into Euclidean Spaces
Explore rigidity of mass-preserving 1-Lipschitz maps from integral current spaces to Euclidean balls, proving isometry conditions and discussing stability of positive mass theorem for graphical manifolds.
Numerical Approaches to Modelling Curved Surfaces
Explore numerical methods for modeling curved surfaces, focusing on applications in physics and biology.
Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Lecture 4
Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
Curvature Tensors and Measures of Singular Spaces - Lecture 3
Explore advanced concepts in geometry, focusing on curvature tensors and measures of singular spaces in this in-depth mathematical lecture.
Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Part II
Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
Geometric Inequalities in Space of Nonpositive Curvature - Part I
Explore geometric inequalities in spaces of nonpositive curvature, focusing on advanced mathematical concepts and their applications.
Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Part I
Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
Curvature Tensors and Measures of Singular Spaces - Part I
Explore curvature tensors and measures of singular spaces in advanced geometry, focusing on concepts beyond Riemannian geometry.
The Feynman Propagator and Self-Adjointness in Wave Operators - Lecture
Explore Feynman and anti-Feynman inverses for wave operators on Lorentzian manifolds, connecting to self-adjointness and positivity properties of wave operators.
Spectral Theory of Stationary Spacetimes - Lecture 4
Explore advanced concepts in spectral theory applied to stationary spacetimes, delving into mathematical relativity and its implications for understanding spacetime structures.
Spectral Theory of Stationary Spacetimes - Lecture 3
Explore advanced concepts in spectral theory of stationary spacetimes, building on previous lectures in the series.
Spectral Theory of Stationary Spacetimes - Part II
Explore advanced concepts in spectral theory applied to stationary spacetimes, building on foundational knowledge in mathematical relativity and quantum mechanics.
One-Loop Renormalizability of the Spectral Action Using Cyclic Cocycles
Explore one-loop renormalizability of the spectral action principle using cyclic cocycles, uncovering its cyclic structure and connections to ribbon graphs in non-commutative geometry.
X-Y Symplectic Transformation in Topological Recursion and Applications - Lecture 3
Explore x-y symplectic transformation in topological recursion and its applications through an advanced mathematical lecture by Alexander Hock.
X-Y Symplectic Transformation in Topological Recursion and Applications - Lecture 2
Explore x-y symplectic transformations in topological recursion and their applications through an advanced mathematical lecture.