New condition found for spherical metrics with conical singularities.
problem Existence of spherical metrics with conical singularities on 2-spheres.
method Sufficient and necessary conditions derived using existing results.
result Necessary condition for spherical metrics with conical singularities.
Odd-dimensional manifolds have contact maps of non-zero degree.
problem Contact domination in odd-dimensional manifolds.
method Proving existence of maps from tight contact manifolds.
result Existence of non-zero degree maps from Liouville-fillable but not Weinstein-fillable contact manifolds.
SIGMA issues a special birthday tribute to Fuchs.
problem N/A
method N/A
result N/A
Smooth surface encloses less volume than a ball.
problem Can a smooth surface enclose less volume than a ball?
method Example of a smooth closed surface in R3 with specific curvature constraints. result No, a supersqueezed sphere encloses less volume than a unit ball.
New shapes enclose less volume than the sphere, surprising in 3D.
problem Finding the minimal volume enclosed by smooth spheres with bounded curvatures.
method Produced a family of bodies parameterized by ε, each bounded by a smooth topological sphere with principal curvatures in [-1, 1].
result The unit sphere does not enclose the minimal volume among all smooth spheres in R^3 with principal curvatures in [-1, 1].
Solves angles and multiplicities for metrics on spheres with singularities.
problem Angles and multiplicities of singularities in metrics on spheres.
method Analyzes Riemannian metrics with conic singularities and co-axial monodromy.
result Completes description of possible angles and multiplicities.
J. Streets and G. Tian recently introduced symplectic curvature flow, a geometric flow on almost Kähler manifolds generalising Kähler-Ricci flow. The present article gives examples of explicit solutions to this flow of non-Kähler structures on several nilmanifolds and on twistor fibrations over hyperbolic space studied…
In this paper, we characterize Riemannian 4-manifold in terms of its almost Hermitian twistor spaces (Z,gt,J±). Some special metric conditions (including Balanced metric condition, first Gauduchon metric condition) on (Z,gt,J±) are studied. For the first Chern form of a natural unitary…
The aim of this paper is to classify simply connected 6-dimensional torus manifolds with vanishing odd degree cohomology. It is shown that there is a one-to-one correspondence between equivariant diffeomorphism types of these manifolds and 3-valent labelled graphs, called torus graphs introduced by Maeda-Masuda-Panov. …
Corrects errors in previous work on spectral asymptotics in elasticity.
problem Two-term asymptotics of elastic eigenvalues on Riemannian manifolds.
method Strongly continuous semigroups and pseudodifferential operators.
result Theorem 1.1 in \cite{Liu-21} is rigorously proven.
The abstract proves the non-existence of certain real algebraic surfaces.
problem The existence of real polynomial functions with specific properties.
method Algebraic solution to a problem proposed by D. A. Panov.
result There does not exist a real polynomial function with the specified properties.
The paper proves conditions for 2-torus manifolds to be equivariantly formal.
problem Characterizing 2-torus manifolds as equivariantly formal.
method Proving 2-torus manifolds are equivariantly formal under specific conditions.
result 2-torus manifolds are equivariantly formal if and only if the action is locally standard and all faces of the orbit space are mod 2 acyclic.
Study spherical conic metrics on Riemann surfaces with isolated singularities.
problem Existence and deformation theory of spherical conic metrics.
method Extended configuration families of simple divisors and Friedrichs extension of the Laplacian.
result Smooth local moduli space of solutions possible when 2 lies in the spectrum of the Laplacian.
Corrects errors in previous work on linear elasticity calculations.
problem Incorrect formulas and conclusions in previous research on linear elasticity.
method Identifying and correcting errors in previous calculations and conclusions.
result Proves the correctness of the main theorem in a previous paper.
Study on closed curves on negatively curved surfaces, linking number formula, and restrictions.
problem Isometric rigidity of tight surfaces and properties of closed asymptotic curves.
method Using Călugăreanu's theorem, derive a formula for the linking number and analyze properties of curves.
result Closed curves with zero linking number cannot have certain planar projections.
LVM and LVMB manifolds are a large family of examples of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a very natural action of the real torus and the quotient of this action is a simple polytope. This quotient allows us to relate c…
LVM and LVMB manifolds are a large family of examples of non kahler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a very natural action of the real torus and the quotient of this action is a simple polytope. This quotient allows us to relate c…
We study Cohen-Macaulay actions, a class of torus actions on manifolds, possibly without fixed points, which generalizes and has analogous properties as equivariantly formal actions. Their equivariant cohomology algebras are computable in the sense that a Chang-Skjelbred Lemma, and its stronger version, the exactness o…
The paper classifies intrinsic torsion in various spacetime structures.
problem Classifying intrinsic torsion in different spacetime structures.
method Review and classification of intrinsic torsion in galilean, Carrollian, Aristotelian, and Bargmannian spacetime structures.
result Found 16 classes for Aristotelian structures and 27 for Bargmannian structures.
Machine learning recreates the periodic table from element properties.
problem Recreating the periodic table using machine learning.
method Unsupervised machine learning with GTM for feature embedding.
result PTG autonomously generates various periodic table layouts.