Mathematics catalogue
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-13051 Boundaries of Groups and Kleinian Groups — Problem 101
- Math-13052 Boundaries of Groups and Kleinian Groups — Problem 107
- Math-13053 Boundaries of Groups and Kleinian Groups — Problem 108
- Math-13054 D. Damanik: Quantum Mechanics and Quasicrystals — Conjecture
- Math-13055 Scalar Curvature Question [?3]: ○What are geometries ofindividual manifoldswith Sc > σ
- Math-13056 Scalar Curvature Question [?4]: ○What are effect of lower boundsSc ≥σ on the topology and geometry of maps between manifolds
- Math-13057 Scalar Curvature Question [?11]: What could be a, possibly non-geometric, extension of the concept ofSc ≥0, where one would be able perform sym
- Math-13058 Scalar Curvature Question [?20]: Also one can possibly relax theisometry at infinitycondition by some "asymptotic flatness" and negativity of a s
- Math-13059 Scalar Curvature Question [?21]: Remove the spin an the uniform positivity conditions, relax completeness and determine the sharp value ofconst
- Math-13060 Scalar Curvature Question [?21]: Evaluate σ○(X0) and σ◻(X0) for "simple" Riemannian manifolds X0 = (X,g 0)
- Math-13061 Scalar Curvature Question [?22]: It seems not impossible, at least for compactX, that, in fact, K-area(X×R) =K-area(X×S1)
- Math-13062 Scalar Curvature Question [?23]: Is the residual finiteness of the fundamental group essential
- Math-13063 Scalar Curvature Question [?25]: (iii) TheSn- andS2-product inequalities seems to hold fornon-trivial sphere fibrations, but I have not checked
- Math-13064 Scalar Curvature Question [?27]: On the other hand, if theδ-neighbourhoods Uδ(S) ⊂X of allT(X)- non-spin surfacesS in a Riemannian manifoldX ar
- Math-13065 Scalar Curvature Question [?28]: For instance, letX be homomorphic to CP 2 and letvol(Uδ(S)) ≥δ2 for allT(X)-non-spin surfacesS ⊂X and 0<δ ≤1
- Math-13066 Scalar Curvature Question [?30]: On the other hand, there probably exist compact simply connected n-dimensional manifolds for alln ≥4 with arbi
- Math-13067 Scalar Curvature Question [?31]: the sharp values ofwidthn−m for these solids remains problematic for m≥2, (unless I missed some paper)
- Math-13068 Scalar Curvature Question [?32]: Waist-Width Inequality
- Math-13069 Scalar Curvature Question [?39]: Let $B=B\Gamma$ be the classifying space of a discrete countable group, and let $f:X\to B$ be a continuous map
- Math-13070 Scalar Curvature Question [?41]: Are there compact manifoldsX which support metricsg withSc(g) > 0 but admit no area extremal or length extrema
- Math-13071 Scalar Curvature Question [?42]: Can one "effectively" evaluate the minimal constantλ=λ(X,g)„ such that a given Riemannin manifoldX = (X,g), e
- Math-13072 Scalar Curvature Question [?43]: Would it be more prudent to replace the conditionSc(g) > 0 byRicci> 0
- Math-13073 Scalar Curvature Question [?45]: Spin Problem
- Math-13074 Scalar Curvature Question [?48]: When does such anX0 is area extremal in the category of complete manifolds
- Math-13075 Scalar Curvature Question [?56]: What are possible values of the co-s+areas of the complements ofr-balls in compact spin manifoldsX withSc(X) ≥
- Math-13076 Scalar Curvature Question [?59]: what is the (asymptotically forn→∞and/or fork→∞) sharp inequality for immersions of theseΣn−1 to spheres
- Math-13077 Scalar Curvature Question [?60]: Also it is unclear if there are (non-trivial) inequalities of this kind for other exotic spheres
- Math-13078 Scalar Curvature Question [?61]: Is then every immersion fromXj to the unit ball in RN satisfies supcurv(Xj↪BN(1) ⊂RN)) ≥ √ k for allN ≥n1+
- Math-13079 Scalar Curvature Question [?67]: This suggests a possibility of definingSc(X) ≥0 for some singular spaces, X, e
- Math-13080 Scalar Curvature Question [?69]: Shrinking of Singularities
- Math-13081 Scalar Curvature Question [?71]: [a] Are the diameters diamc(Lip1(Bn(R)→S))) bounded for a large fixedc and R →∞if Hi(S, R) = 0 for i = 1, 2,
- Math-13082 Scalar Curvature Question [?72]: [b] What is the asymptotics of the diameters diamc(Lip1(Bn H(R)→S))) for the hyperbolic ballsBn H(R) and R→∞
- Math-13083 Scalar Curvature Question [?74]: Parametric Hypersphericity
- Math-13084 Scalar Curvature Question [?75]: If m = n−1 then, conjecturally, this is the only manifold with this property: the inequalities macr
- Math-13085 Scalar Curvature Question [?79]: InvarianceandNon-invarianceof Sc∩(Y ) = +∞
- Math-13086 Scalar Curvature Question [?87]: but there are no apparent examples (if any) where these inequalities are strict
- Math-13087 Scalar Curvature Question [?90]: Hyperbolic Volume Inequality
- Math-13088 Toral manifolds and positive scalar curvature — Question 2
- Math-13089 Coarse embeddings
- Math-13090 Coarse embeddings — Question 2
- Math-13091 Classification problems and Poisson structures
- Math-13092 Closed geodesics
- Math-13093 Configuration Spaces of Tensegrities — Problem 8
- Math-13094 Geometry of Curves and Surfaces — Problem 1.4
- Math-13095 General elephant problem
- Math-13096 The McMullen problem on projectively transforming sets of points into convex position
- Math-13097 Is there a general expression for how much the ends of a long rope of radius 1 get closer when a tight open knot is tied into it
- Math-13098 The universality spectrum problem
- Math-13099 Does a finitely presented homogeneous structure for a finite relational language have finitely many reducts
- Math-13100 Is there a logic L which satisfies both the Beth property and Δ-interpolation, is compact but does not satisfy the interpolation property