A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study improves bounds on p-covectors and proves stable systolic inequalities.
A new method using mod n covering improves systolic inequalities.
Sharp inequalities for Kähler manifolds' systolic invariants are established.
Multiplicative relations in the cohomology ring of a manifold impose constraints upon its stable systoles. Given a compact Riemannian manifold (X,g), its real homology H_*(X,R) is naturally endowed with the stable norm. Briefly, if h\in H_k(X,R) then the stable norm of h is the infimum of the Riemannian k-volumes of re…
We show that for closed orientable manifolds the -dimensional stable systole admits a metric-independent volume bound if and only if there are cohomology classes of degree that generate cohomology in top-degree. Moreover, it turns out that in the nonorientable case such a bound does not exist for stable systoles…
Paper proves optimal systolic inequality for manifolds with positive triRic curvature.
Sharp inequality for complex projective space's systoles under scalar curvature bounds.
Upper bound found for systolic geometry on manifolds with positive scalar curvature.
It follows from a theorem of Gromov that the stable systolic category of a closed manifold is bounded from below by the rational cup-length of the manifold. In the paper we study the inequality in the opposite direction. In particular, combining our results with Gromov's theorem, we prove the equality of stable systoli…
Withdrawn by first author.
We generalize optimal inequalities of C. Loewner and M. Gromov, by proving lower bounds for the total volume in terms of the homotopy systole and the stable systole. Our main tool is the construction of an area-decreasing map to the Jacobi torus, streamlining and generalizing the construction of the first author in col…
A new systolic inequality with a remainder for the real projective plane.
Extends Gromov's optimal systolic inequality to manifolds with specific cohomology properties.
New systolic inequality for 3D contact forms on Seifert bundles.
Extended systolic inequality for 2-complexes to improve group systolic area bounds.
A new systolic inequality for mod 2 systoles is established.
Sharp inequalities link manifold's systole to curvature of boundary.
Sharp systolic inequality for invariant tight contact forms on S1-bundles over S2.
The paper proves optimal systolic inequalities for Möbius strip and Klein bottle.
New bounds set for stable 2-systole in specific geometric spaces.
We prove the simultaneous (k,n-k)-systolic freedom, for a pair of adjacent integers k smaller than n/2, of a simply connected n-manifold X. Our construction, related to recent results of I. Babenko, is concentrated in a neighborhood of suitable k-dimensional submanifolds of X. We employ calibration by differential form…
Introduces systolic inequalities in Riemannian and symplectic geometry.
The article disproves a local systolic inequality and shows a lower bound on filling area.
The study proves surfaces with high genus have a specific inequality.
Sharp inequalities found for orbifold metrics.
Study systoles and diameters on hyperbolic surfaces, finding an upper bound for their ratio.
We prove optimal systolic inequalities on Finsler Mobius bands relating the systole and the height of the Mobius band to its Holmes-Thompson volume. We also establish an optimal systolic in- equality for Finsler Klein bottles of revolution, which we conjecture to hold true for arbitrary Finsler metrics. Extremal metric…
Two lectures on metric geometry of manifolds.
Optimal systolic inequality proved for manifolds with positive bi-Ricci curvature.
We establish combinatorial versions of various classical systolic inequalities. For a smooth triangulation of a closed smooth manifold, the minimal number of edges in a homotopically non-trivial loop contained in the -skeleton gives an integer called the combinatorial systole. The number of top-dimensional simplices…
Proves a new inequality for certain complex surfaces.
We show that the systolic constant, the minimal entropy, and the spherical volume of a manifold depend only on the image of the fundamental class under the classifying map of the universal covering. Moreover, we compute the systolic constant of manifolds with fundamental group of order two (modulo the value on the real…
Positive scalar curvature implies small 2-systoles in Kähler manifolds
3D contact manifolds have optimal higher systolic ratios.
Optimal inequalities for systole, inradius, and volume in hyperbolic 3-manifolds
We investigate the filling area conjecture, optimal systolic inequalities, and the related problem of the nonvanishing of certain linking numbers in 3-manifolds.
Tight embeddings of 2-tori in 3D space contain short loops.
We show that the geometry of a Riemannian manifold (M,g) is sensitive to the apparently purely homotopy-theoretic invariant of M known as the Lusternik-Schnirelmann category, denoted cat_{LS}(M). Here we introduce a Riemannian analogue of cat_{LS}(M), called the systolic category of M. It is denoted cat_{sys}(M), and d…
We give a short proof of the systolic inequality for the n-dimensional torus. The proof uses minimal hypersurfaces. It is based on the Schoen-Yau proof that an n-dimensional torus admits no metric of positive scalar curvature.
We prove a new systolic volume lower bound for non-orientable n-manifolds, involving the stable 1-systole and the codimension 1 systole with coefficients in Z_2. As an application, we prove that Lusternik-Schnirelmann category and systolic category agree for non-orientable closed manifolds of dimension 3, extending our…
In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider some features of the forgetful map from the above moduli space of spherical sur…
We introduce the notions of categorical systoles and categorical volumes of Bridgeland stability conditions on triangulated categories. We prove that for any projective K3 surface, there exists a constant C depending only on the rank and discriminant of its Picard group, such that $$\mathrm{sys}(σ)^2\leq C\cdot\mathrm{…
We study optimal curvature-free inequalities of the type discovered by C. Loewner and M. Gromov, using a generalisation of the Wirtinger inequality for the comass. Using a model for the classifying space BS^3 built inductively out of BS^1, we prove that the symmetric metrics of certain two-point homogeneous manifolds t…
Loewner inequality proven for curved surfaces.
We define Dirichlet type series associated with homology length spectra of Riemannian, or Finsler, manifolds, or polyhedra, and investigate some of their analytical properties. As a consequence we obtain an inequality analogous to Gromov's classical intersystolic inequality, but taking the whole homology length spectru…
Paper proves constants for Moser-Trudinger inequality on surfaces.
This is an expository essay about systolic geometry. It describes a central theorem in the subject and why the proof is difficult. Then it discusses different metaphors which suggest ways to approach the problem. The metaphors connect the systolic inequality to minimal surfaces, topological dimension, scalar curvature,…
We prove an optimal systolic inequality for CAT(0) metrics on a genus~2 surface. We use a Voronoi cell technique, introduced by C.~Bavard in the hyperbolic context. The equality is saturated by a flat singular metric in the conformal class defined by the smooth completion of the curve y^2=x^5-x. Thus, among all CAT(0) …