
Explore novel proofs and techniques in metric p-Sobolev spaces, connecting plans, derivations, and currents in metric measure spaces. Gain insights into advanced mathematical concepts.

Explore p-energy forms in Cheeger spaces without relying on gradients. Learn about constructing these forms using characteristic features of Cheeger metric measure spaces.

Explore Riesz transforms in tamed Dirichlet spaces, examining Lp-boundedness under distributional curvature lower bounds and gaugeability conditions.

Explore Sobolev spaces in extended metric-topological measure spaces, focusing on Cheeger energy construction and properties in this general framework.

Explore sharp isoperimetric-type inequalities in Lorentzian spaces with time-like Ricci curvature bounds, including applications to black holes and cosmological space-times.

Explore integral Varadhan formula for nonlinear heat flow on measured Finsler manifolds, examining particle probability and distance relationships in geometric analysis.

Explore gradient estimates and functional inequalities on sub-Riemannian manifolds, focusing on techniques like tensorisation and quotients for spaces without curvature bounds.

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.

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.

Explore formulas for binomial, geometric, Poisson, uniform, and exponential probability distributions. Master key concepts to solve statistical problems effectively.

Explore numerical methods for modeling curved surfaces, focusing on applications in physics and biology.

Explore advanced concepts in set theory, focusing on longer Prikry sequences and their implications in mathematical logic and forcing axioms.

Explore almost disjoint families in natural models of AD+, delving into determinacy, inner models, and forcing axioms in mathematics.

Explore ladder mice in mathematics with Farmer Schlutzenberg, delving into determinacy, inner models, and forcing axioms.

Explore Martin's Maximum c*,++ in Pmax extensions of strong determinacy models, delving into advanced set theory concepts and their implications.

Explore the HOD conjecture's intricacies and its ultimate failure in set theory, delving into advanced mathematical concepts and their implications.

Explore singular cardinals, square principles, and linear orders in set theory, examining Todorcevic's result and related PCF-theoretic principles.

Explore unreachability in the second projective-like hierarchy with Derek Levinson's advanced mathematical analysis.

Explore forcing and consistency properties in set theory, delving into advanced mathematical concepts and their applications.

Explore characterizations of large cardinals using Löwenheim-Skolem and weak compactness properties in infinitary second-order logic, including recent work on Shelah cardinals.

Explore Chang's Conjecture and Mouse Reflection in mathematics, delving into advanced concepts from set theory and logic.