Papers nuevos sobre Geometría y topología
266 papers nuevos sobre geometría y topología en los últimos 7 días, dentro de Matemática y estadística. Acá están los 50 que Pipette considera más valiosos, con el resultado principal en palabras de sus autores.
Lo mejor de la semana
A Spectral Proof of Khachiyan's Ellipsoid Conjecture
We prove that every closed halfspace whose boundary passes through the center of the maximizing ellipsoid satisfies \[ w(K\cap H)\le\frac{\sqrt e}{2} w(K).
PreprintDice ser un gran avanceCódigo disponibleMinimal equatorial fillings
We show that a great circle in bounds embedded non-orientable minimal surfaces of unbounded genera and all possible non-zero Euler numbers.
PreprintDice ser un gran avancePositive Sectional Curvature on All Smooth 7-spheres
We construct a smooth Riemannian metric with strictly positive sectional curvature on every smooth homotopy seven-sphere.
PreprintDice ser un gran avanceA set of points with optimal spherical cap discrepancy
In particular, for , Stolarsky's invariance principle implies that has spherical cap discrepancy of asymptotically optimal order \[ D_{L^2}^C(\mathcal P_N)\asymp N^{-3/4}, \] making it, to our knowledge, the first explicit configuration proved to have this property.
PreprintDice ser un gran avanceExponential improvements in Rado's covering problem
Here we offer the first exponential improvement of the lower bound in almost 80 years, which narrows the gap to: \[ 2.910^{-d} \leq f(B^d) \leq 2.447^{-d}.
PreprintPrescribed singular sets for stationary harmonic maps
In this paper, we construct counterexamples to this folklore conjecture.
PreprintDice ser un gran avanceType changing, compact generalized Calabi--Yaus
We provide the first compact examples of type-changing generalized Calabi--Yau manifolds using Fei's construction of non-K\"ahler Calabi--Yau manifolds on branched covers of twistor spaces \cite{Fei16}.
PreprintDice ser un gran avanceA Multidimensional Birkhoff Theorem for some Lagrangians
We prove a multidimensional Birkhoff theorem for a new class of " Lagrangian subsets" in cotangent bundles, obtained as Hausdorff limits of compact exact Lagrangian submanifolds with control on their Liouville primitives.
PreprintDice ser un gran avanceFractional illumination and the optimal exponential rate in Hadwiger's covering conjecture
We also prove that every such body can be covered by at most smaller positive homothetic copies as , establishing the optimal exponential rate in Hadwiger's covering conjecture.
PreprintAmple vector bundles without Griffiths-semipositive metrics
We construct a rank-two ample holomorphic vector bundle on an abelian surface that admits no smooth Griffiths-semipositive Hermitian metric, thereby giving a counterexample to the Griffiths conjecture.
PreprintDice ser un gran avanceOn the degenerate Weyl problem on isometric immersions
We establish two results on the degenerate Weyl problem, namely when the Gaussian curvature is only nonnegative rather than strictly positive.
PreprintDice ser un gran avanceNonsmoothable Embedded Surfaces in 4-Manifolds That Become Smoothable after a Single Stabilization
In this paper, we find infinitely many examples of nonsmoothable embedded surfaces in a 4-manifold that become smoothable after taking the connected sum with S^2 x S^2.
PreprintMilnor's inequality and circular elastic knots
We establish the extension of Milnor's inequality, relating total curvature with the bridge index, to the -closure of a knot class, without any restriction on the self-intersections of the limit curve.
PreprintReflective projective billiards in the plane: odd periods, period five, and metric rigidity
We give a single explicit family with an open set of periodic trajectories for every period at least three, including every odd period, and identify the previously known centrally projective examples as a special parameter value.
PreprintQuasihyperbolic domains are CAT(2)
We prove that every proper subdomain of the Euclidean space equipped with its quasihyperbolic metric is CAT(2).
PreprintChain-level decoupling of the physical heterotic deformation complex at the standard embedding
We give an explicit chain-level decoupling of its first-order coefficient complex at the minimal standard embedding, where the gauge bundle is the tangent bundle, the gauge connection is the Levi--Civita connection, and the background structure is torsion-free.
PreprintExistence of disks with prescribed mean curvature and contact angle in arbitrary codimension
Under suitable relative homotopy and boundary admissibility assumptions, we establish a min-max theory in arbitrary codimension that produces nonconstant branched immersed disks or spheres in closed Riemannian manifolds, with controlled Morse index, where the prescribed mean curvature type tensor and the nonorthogonal, nonconstant contact angle condition of disks along a supporting submanifold are determined by the same differential 2-form.
PreprintThe dHYM equation on crepant resolutions of Calabi-Yau cones
As an application, we show that every holomorphic line bundle over admits a smooth, globally defined Hermitian connection solving the dHYM equation, provided the total phase lies in an explicit open interval determined by the Lie-theoretic data.
PreprintRicci entropy, RCD structures and Kahler spaces
We show that a lower bound for the Ricci current in the sense of pluripotential theory is equivalent to a synthetic Ricci lower bound in the sense of RCD theory.
PreprintA Differential-Geometric Framework for Risk-Optimal Asset Reallocation
We develop a differential-geometric framework for risk-optimal portfolio reallocation.
PreprintA proof of the Willmore-type conjecture in
In this paper, we confirm this conjecture in the Lagrangian setting and disprove it in the general setting.
PreprintGeometric flows of branched transportation networks
We construct a geometric flow of transportation networks, which correspond to normal real -rectifiable currents, by modifying Brakke's variational approximation scheme.
PreprintA Conditional Oka Complex Structure of the Six-Sphere
We prove that is an Oka manifold.
PreprintKakeya and Furstenberg problems for sticky sets of tubes
In the second part, we prove the Kakeya set conjecture in for sticky sets of tubes satisfying convex Wolff axioms.
PreprintFrom Dimension Drop to Aperiodic Order
We synthesise these three perspectives to obtain a complete topological classification of for .
PreprintLocal coefficients for genuine equivariant cohomology I
We develop a theory of equivariant local systems which categorifies genuine equivariant cohomology theories -- such as Atiyah--Segal -theory, Lurie's tempered cohomology, and the equivariant elliptic cohomology of Grojnowski, Greenlees, and Gepner--Meier -- analogously to how the category of ordinary local systems categorifies singular cohomology.
PreprintImproved bounds for universal convex covers of unit arcs
We show that the infimum area among convex universal covers satisfies , reducing the gap between the previous refereed bounds by over .
PreprintCódigo disponibleMaximal first Betti number drop and collapsing RCD spaces
Their first Betti numbers can drop by at most .
PreprintUniform RC-positivity of tangent bundles
In this paper, we prove that every rationally connected projective manifold admits a smooth uniformly RC-positive Hermitian metric on its tangent bundle, answering Yang's question and giving a characterization of rational connectedness by uniform RC-positivity.
PreprintHopf Reduction and Multiplicity-Resolved Endpoints for the Classical Willmore Flow of Hopf Tori
We establish an exact parametrized reduction of the classical Willmore flow of Hopf tori in the round three-sphere to the spherical elastic flow.
PreprintGeometric ideal triangulations of hyperbolic 3-manifolds
We resolve the longstanding geometric ideal triangulation conjecture arising from Thurston's theory of hyperbolic 3-manifolds: every finite-volume cusped hyperbolic 3-manifold admits a finite geometric ideal triangulation realizing its complete hyperbolic structure.
PreprintDice ser un gran avanceBlaschke Conjecture and Complex Geometry
Combining this with Hwang-Mok VMRT recognition, we prove the Blaschke conjecture for manifolds admitting an adapted complex structure on their entire tangent bundles.
PreprintDescartes' Circle Theorem, Princess Elizabeth, and Spinors
In this article, on Descartes' famous "circle theorem," we first attempt to explain how the philosopher could have arrived at the equation that he presents without demonstration in a letter to Princess Palatine Elizabeth of Bohemia in November 1643 (a previously unpublished proof, to our knowledge).
PreprintAsymmetric L-space knots with arbitrary braid index
In this paper, we construct an asymmetric hyperbolic L-space knot with arbitrary braid index bigger than 4.
PreprintBimeromorphic invariance of -property and blow-up formulae I: counterexamples and derived category approach
Using N. Honda's construction of twistor spaces, bimeromorphic invarince of -lemma for threefolds and embedded resolution, we find a smooth compact complex threefold satisfying the -lemma that contains a smooth compact surface for which the lemma fails.
PreprintALH Gravitational Instantons and Rational Surfaces
We construct complete ALH hyperk\"ahler metrics on complements of anticanonical elliptic curves with zero self-intersection in smooth rational surfaces.
PreprintThe metric extension problem under positive and negative curvature conditions
We first prove that every smooth boundary metric on a compact manifold extends to a metric with any prescribed positive lower bound for Ricci curvature, whereas extensions under stronger positive \(k^{th}\)-intermediate Ricci curvature conditions may fail due to local obstructions.
PreprintA gluing construction of -extremal K\"ahler metrics and new examples of Bismut Hermitian-Einstein -folds
We present a gluing construction for a class of 6th order geometric non-linear PDE's on a K\"ahler manifold or orbifold, arising in the study of Bismut Hermitian Einstein complex -folds, the supersymmetric and solutions of type IIB and supergravity models in physics, and in Dervan's Z-critical K\"ahler metrics.
PreprintQuantitative asphericalization and Gromov's linear bordism problem
We prove a PL bordism version of Gromov's linearity conjecture over a broad class of asphericalization groups for manifolds endowed with faithful representations in all dimensions.
PreprintWeighted normalized curve shortening flow with applications in pseudo-Euclidean spaces
Applying to closed smooth spacelike curves in pseudo-Euclidean spaces that admit a one-to-one convex projection onto a spacelike plane, at their finite maximal time we will see: either the curve shrinks to a point and becomes asymptotically circular, or the tangent directions subsequentially approach the null cone. Both alternatives occur.
PreprintMeasure contraction property on isometric leaves and monotone fibres
For finite measures with positive densities on convex Euclidean supports, we prove that passes with unchanged parameters to almost every isometric leaf of an arbitrary nonexpansive map.
PreprintFiniteness of closed arithmetic hyperbolic surface bundles
For each , we show that there are finitely many cyclic commensurability classes of closed, fibered arithmetic hyperbolic -manifolds with genus fiber.
PreprintUniversal Spacelikeness Estimates and Liouville Rigidity for Lorentzian Curvature Equations
For and , we prove that every such solution vanishes identically, without symmetry, decay, integrability, or curvature pinching assumptions.
PreprintRigidity of nonsteady gradient K\"ahler-Ricci solitons with constant scalar curvature
We prove that every complete nonsteady gradient K\"ahler-Ricci soliton with constant scalar curvature is rigid.
PreprintOn random diameters of convex bodies
In this work, we study the diameters of random sections of and derive upper and lower bounds for them in terms of geometric parameters of .
PreprintK\"ahler Rigidity for Constant Chern Holomorphic Sectional Curvature
We prove two rigidity theorems for compact Hermitian manifolds with constant Chern holomorphic sectional curvature.
PreprintThe sharp isoperimetric inequality for varifolds in codimension two
We prove a Michael-Simon inequality for a class of varifolds in Euclidean space that includes all integral varifolds with locally bounded first variation of arbitrary dimension and codimension.
PreprintUniruledness and the sign of total scalar curvature
For every integer , we construct a smooth projective manifold of complex dimension whose canonical bundle is not pseudoeffective, or equivalently, which is uniruled, but every K\"ahler metric has negative total scalar curvature.
PreprintEstablishing the Polynomial Wolff Axioms for -Separated -Tubes With #o-minimality
We establish the full version of a conjecture of Guth and Zahl, giving a lower bound for the volume of a semialgebraic set that has a large intersection with a collection of -separated -tubes.
PreprintLarge signed sums of unit vectors: the first linearly dependent case
\] We prove that this value is .
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