Mathematics Problem Archive

; Do CMC spheres about a point $x$ in such a space form a foliation of $X-\{x\}$?; Could this be a way of proving embeddedness of CMC spheres in gener...

; Calabi-Yau problem. For an embedded minimal surface in $\mathbb{R}^3$, does complete imply proper?; Hoffman-Meeks conjecture. For a complete embedde...

Is every Laplacian algebra of polynomials maximal?...

Prove the lower bound \[ d\le \mbox{Index}(\Phi_{\mathcal A})+\mbox{Null}(\Phi_{\mathcal A}), \] where $\mbox{Null}(\Phi_{\mathcal A})$ is the {\it nu...

Prove that there exists infinitely many distinct minimal branched 2-dimensional immersions in $N^n$....

Does the normalized Ricci flow converge in Gromov-Hausdorff sense to a generalized K\"ahler-Einstein space?...

Does Frankel's theorem hold for symmetric Finsler metrics?...

Is this true without the bumpy assumption?...

Describe the combinatorics of B2(K6); B3(K4) and B3(K5)....

Describe all the possible different types of strata for 10 points....

Compute the number of different types of strata for n points with arbitrary n. 4 OLEG KARPENKOV v1 v2 v3v4 v5 v6 K3;3 q1 q2 q3 p1 p2 p3 p4 p5 p6 q3 q2 ...

Which subgraphs of Kn define the same stratifications?...

Find all strata of codimension more than 1 that are not defined as an intersection of the closure of several codimension 1 strata....

Which Cayley algebra systems define the same strata?...

Given a graph G. Does there exist a Cayley algebra system (or several systems) describing the union of the codimension 1 tensegrity strata in the plan...

Write (if exist) Cayley algebra systems defining the strata for the following graph: Currently this example is a strong candidate for a counterexample ...

Develop theory of geometric conditions for strata in multidimensional case....

Does there exist a closed C2 surface in Euclidean space R3 which is flexible?...

Are all smooth tight surfaces in R3 rigid?...

Are negatively curved annuli bounded by a pair of fixed convex planar curves rigid?...

Let Γ be a smooth closed curve immersed in R3. Suppose that Γ has a continuous binormal vector field B which is one-to-one. Does it follow then that th...

Given a metric of positive curvature on the disk what is the condition on a space curve to form the boundary of an isometric embedding of the disk?...

Does every curve bounding a surface of positive curvature in 3-space have (at least) four points where the torsion vanishes?...

Are there some nonconvex surfaces which remain rigid after finitely many points of them have been deleted. For instance, are punctured analytic tight s...

(The global isometric embedding problem, Yau [189] 1993; Gromov [82]). Can everyC∞ 2-dimensional Riemannian manifold be isometrically embedded in R4?...

Given a C∞ metric in a neighborhood of a point in a 2-dimensional Riemannian manifold, does there exist an isometric embedding of some neighborhood of...

For which setsA⊂ Sn is there an immersionf: M→ Rn+1 such that Gf(M)⊂A?...

Does connectedness of the shadows imply that f(M) is convex?...

LetM,M′⊂ R3 be smooth orientable closed surfaces. Suppose there exists a diffeomorphism f: M→ M′ which preserved the Gauss curvature and the Gauss map....

LetP, P′⊂ R3 be polyhedral surfaces. Suppose that the faces of P and P′ are parallel and have the same area. Does it follow then that P and P′ are con...

Is every convex polytope unfoldable?...

Does there exist a reasonably simple algorithm for detecting the edges of a convex polyhedron intrinsically?...

Does there exist a convex polyhedron with a pseudo edge graph which is not unfoldable....

Of all convex surfaces with a fixed intrinsic diameter, is the one with the greatest area a doubled disk?...

Let S ⊂ R3 be a closed surface of constant width and fixed area. How small can the volume of S be?...

LetS⊂ R3 be a closed surface of diameter d. Suppose that there exists a constant h < dso that whenever a pair of planes separated by a distance of h i...

What is the shortest curve in R3 with a given width or inradius?...

Let $\Gamma$ be a closed curve of fixed length $L$ in $\mathbb{R}^3$. Determine the maximum possible volume of the convex hull of $\Gamma$....

Let $\Gamma$ be a closed curve of fixed length $L$ in $\mathbb{R}^3$, and let $A$ be the area of its convex hull. Prove that $A$ is maximized when $\G...

Is every compact connected minimal surface bounded by a pair of convex planar curves topologically an annulus?...

Does there exist an embedded compact surface of constant mean curvature which is bounded by a circle, but is not a piece of a sphere....

Show that any compact embedded CMC surface which is bounded by a convex planar curve, and lies on one side of the boundary plane, is topologically a d...

Are there any complete surfaces of negative curvature in Euclidean 3-space whose principal curvatures are bounded away from zero?...

Are there any complete negatively curved surfaces embedded in the unit ball?...

Does there exist any complete negatively curved surfaces with negative Euler characteristic contained in between a pair of parallel planes in R3....

Show that the index of any singularity of a principal line fields on a surface is at most one....

Let M be a complete noncompact convex surface in R3, with principal curvatures k1, k2, then show that inf M|k1−k2| = 0....

Bass conjecture: for every finitely generated $\mathbb Z$-algebra $A$ and every $n\geq0$, is the G-theory group $K'_n(A)$ finitely generated? Equivale...

Bass–Quillen conjecture: if $A$ is a regular Noetherian ring, is every finitely generated projective module over $A[t_1,\ldots,t_n]$ extended from a p...

Deligne's conjecture on Hochschild cohomology about the operadic structure on Hochschild cochain complex....