Quantum geometry gives a regularization scheme-independent effective action, whoes equation of motion for the conformal mode has a stable de Sitter solution at the high-energy region where the coupling of the self-interactions of the traceless mode...
Variational geometries describing corrugated graphene sheets are proposed. The isothermal thermomechanical properties of these sheets are described by a 2-dimensional Weyl space. The equation that couples the Weyl geometry with isothermal distributio...
We establish some connections between nonresonant $A$-hypergeometric systems and de Rham-type complexes. This allows us to determine which of these $A$-hypergeometric systems "come from geometry."...
Geometry is a branch of mathematics that includes the study of shape, size, and other properties of figures. It is one of the oldest branches of mathematics and may have been used even in prehistoric …
Feb 10, 2025 · Geometry is a branch of mathematics that deals with the study of shapes, sizes, and the properties of space. It focuses on the relationships between points, lines, surfaces, and solids in a …
Interactive, free online geometry tool from GeoGebra: create triangles, circles, angles, transformations and much more!
Feb 3, 2026 · Geometry, the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.
Learn geometry—angles, shapes, transformations, proofs, and more.
For a smooth projective curve, the cycles of subordinate or, more generally, secant divisors to a given linear series are among some of the most studied objects in classical enumerative geometry. We consider the intersection of two such cycles corres...
This is our reply to "Comment on 'Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling', arXiv:2305.02340, J. Yu, C. J. Ciccarino, R. Bianco, I. Errea, P. Narang, B. A. Bernevig" by Prof. Pickett, which focuses on the MgB$_2$ part...
We present a novel appearance model that simultaneously realizes explicit high-quality 3D surface mesh recovery and photorealistic novel view synthesis from sparse view samples. Our key idea is to model the underlying scene geometry Mesh as an Atlas...
Looking at the geometry across the different sizes of the Stinner Frameworks Refugio, it seems like their 52cm is closer to what many other brands would call a 56cm. For example, the listed reach on t...
We study the geometry of point-orbits of elation groups with a given center and axis of a finite projective space. We show that there exists a 1-1 correspondence from conjugacy classes of such groups and orbits on projective subspaces (of a suitable...
Opportunity cost matrices are interesting in the context of scenario reduction. We provide new algorithms, based on ideas from algebraic geometry, to efficiently compute the opportunity cost matrix using computational algebraic geometry. We demonstra...
The length and bore geometry of musical instruments directly influences the quality of sound that can be produced. In brass instruments, nonlinear effects from finite-amplitude wave propagation can lead to wave distortion giving sounds a brassy timbr...
Considered one of the founding fathers of integral geometry, Luis Santaló has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic geometry, in functional ana...
In this paper, we classify hypersurfaces with constant principal curvatures in the four-dimensional Thurston geometry ${\rm Sol_0^4}$ under certain geometric conditions. As an application of the classification result, we give a complete classificatio...
We provide a detailed analysis of the doubly spinning black ring, investigating both its general properties and its shape. We also examine the geometry of the ergosurface, illustrating the process of self-merging and discussing the physics of ergor...
We give a description of the intrinsic geometry of elastic distortions in three-dimensional nematic liquid crystals and establish necessary and sufficient conditions for a set of functions to represent these distortions by describing how they couple...
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric entities like...