Uniform Volume Doubling and Functional Inequalities on Lie Groups
Explore functional inequalities on Lie groups, focusing on uniform volume doubling and its implications for SU(2) and related structures. Gain insights into heat kernel estimates and measure contracting properties.
Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds
Explore the interaction between hyperbolic geometry and homology cobordism in low-dimensional topology using monopole Floer homology to study subgroups of the homology cobordism group.
Conjugate Points and the MC Criterion in Volume-Preserving Diffeomorphisms - Lecture
Explore conjugate points on volume-preserving diffeomorphisms, focusing on the MC criterion and its applications in fluid dynamics and Riemannian geometry.
Comparing Oresme's Curvitas with Riemann's Curvature
Explore the historical evolution of curvature concepts from Oresme's 14th-century insights to Riemann's geometric definitions, examining their mathematical and philosophical implications.
Width, Scalar Curvature and Macroscopic Scalar Curvature
Explore the interplay between positive scalar curvature and macroscopic scalar curvature, examining Urysohn width and closed geodesics in PSC and PMSC spaces.
Spectra of Laplace and Dirac Operators on Noncompact Manifolds
Explore spectra of Laplace and Dirac operators on complete manifolds, including types of spectra, results for special behaviors at infinity, and effects of additional potentials.
Another Aspect of Gromov's Conjectures on Scalar Curvature
Explore Gromov's scalar curvature conjectures through general relativity, examining partial solutions via the positive mass theorem.
Geometric Variational Methods for Scalar Curvature and Other Curvature Problems
Explore geometric variational problems and their applications to curvature conditions, focusing on Schoen-Yau's approach and recent extensions.
Stability of Llarull's Theorem in All Dimensions
Explore stability of Llarull's theorem in all dimensions using spin geometry, with results in intrinsic flat and C^0-convergence outside small sets.
Global Effects of Positive Scalar Curvature in Geometry
Explorez les effets globaux de la courbure scalaire positive, y compris le problème de remplissage de Gromov et les théorèmes de type Llarull sur les variétés complètes.
Positive Mass Theorem and Positive Scalar Curvature with Singularities
Explore recent developments in positive mass theorem and scalar curvature, focusing on singular metrics and isolated conical singularities in mathematical physics.
Positive Scalar Curvature with Point Singularities
Explore topological construction of positive scalar curvature metrics with Euclidean point singularities, challenging Schoen's conjecture and geometric flow limitations.
Distance, Curvature and Symmetry - A Haphazard Tour Through Metric Geometry
Explore metric geometry through distance, curvature, and symmetry concepts, gaining insights into fundamental mathematical principles and their applications in spatial analysis.
Linear Programming Bounds for Hyperbolic Surfaces - Seminar on Spectral Geometry
Explore linear programming bounds for hyperbolic surfaces, examining closed geodesics and Laplace eigenvalues. Gain insights into quantitative behavior and predominance in Riemannian metrics.
Eigenvalues and Minimal Surfaces
Explore Laplace operator eigenvalues, their physical significance, and connection to minimal surfaces. Discover recent findings in isoperimetric eigenvalue problems for Riemannian surfaces.
New Minimal Surfaces via Equivariant Eigenvalue Optimization - Part II
Explore equivariant optimization of Laplace and Steklov eigenvalues on surfaces to construct embedded minimal surfaces in 3-sphere and 3-ball. Discover new insights into geometric analysis and topology.
Scalar Curvature Rigidity of Polytopes
Explore Riemannian metrics and scalar curvature positivity in differential geometry. Delve into Gromov's comparison principle for polytopes and recent advancements in verifying his conjecture.
Singularity Models in 3D Ricci Flow
Explore singularity formation in 3D Ricci flow, examining recent developments leading to a complete classification of singularity models beyond Perelman's breakthrough.
Steklov Eigenvalues in Negatively Curved Manifolds
Explore Steklov eigenvalue problem in negatively curved manifolds, focusing on lower bounds and relationships with volume and boundary area in dimensions 3 and higher.
Positive Scalar Curvature on Manifolds and Foliations - ICBS 2024
Explore recent advances in positive scalar curvature metrics on manifolds and foliations, a key topic in differential geometry.
Critical Metrics of Eigenvalue Functionals via Subdifferential
Explore critical metrics of eigenvalue functionals using subdifferential, covering Laplace and Steklov eigenvalues and offering new perspectives on Riemannian geometry.