Latest Articles for Geometry

This article introduces a geometrical framework for understanding quantum states and their changes.

This article discusses applying Steiner symmetrization to spherical shapes to enhance their properties.

Explore the relationship between metric structures and ultracategories in mathematics.

Exploring how light reflects in elliptical billiard tables and the significance of cusps.

Explore the complex relationships in signed projective cubes and their impact on mathematics.

Explore the unique properties of projective rectangles in geometry.

A look into the relationships between fundamental concepts in algebraic geometry.

An overview of creating minimal surfaces using pentagonal shapes and their applications.

A look into the complexities of non-commutative integration in two-dimensional spaces.

Explore the interaction of curves with complete intersections in geometry.

Exploring methods to extend functions in Sobolev spaces across various structures.

An overview of minimal submanifolds in Riemannian symmetric spaces.

A look into exact categories and their role in algebra and geometry.

Explore Grassmannians and their role in geometry and curvature analysis.

Exploring the role of triple grid diagrams in understanding surfaces and links in mathematics.

A look into knot theory, focusing on properties, invariants, and torsion elements.

A closer look at the properties and applications of braided Hopf algebras.

A concise overview of polytopes, their graphs, and symmetries.

Exploring the links between polyhedral products, toric geometry, and motivic homotopy theory.

Understanding sphere arrangements and their mathematical implications in higher dimensions.

An insight into the shape-shifting world of flexible polyhedra.

Exploring the limitations of the quadratrix in achieving circle squaring.

A look into gravitational instantons and their mathematical properties.

Exploring unique surfaces defined within a bi-complex hyperbolic framework.

Explore the links between root polytopes and quivers in mathematical studies.

An overview of lattices, commensurability, and their significant properties in mathematics.

Exploring the connection between Iwahori groups and symmetric spaces in mathematics.

A look into the Heisenberg group and its impact on sub-Riemannian geometry.

Analyzing polynomial-like behavior of Laplace eigenfunctions in small regions.

Exploring the relationships in noncommutative algebra and its applications across disciplines.

Exploring the complexities of operator algebras and their representations.

Exploring the role of curved tetrahedra in quantum physics and gravity.

Exploring the relationship between symplectic and algebraic geometry through homological mirror symmetry.

A clear look at symplectic geometry and its link to Hermitian symmetric spaces.

Explore the fascinating world of Iterated Function Systems and their intricate shapes.

A novel method for building special four-dimensional shapes in geometry and gravity.

Investigating optimal shapes in geometry using double and triple bubbles.

This paper examines isolated points in the moduli space of special Lagrangian submanifolds.

A look into five-dimensional theories and their geometrical properties in physics.

Explore the impact of blowup techniques on Lie algebroids and their cohomology.