Related papers: No skew branes on non-degenerate hyperquadrics
We prove that in Euclidean space $R^{n+1}$ any compact immersed nonnegatively curved hypersurface $M$ with free boundary on the sphere $S^n$ is an embedded convex topological disk. In particular, when the $m^{th}$ mean curvature of $M$ is…
We study non-degenerate CR geometries of hypersurface type that are symmetric in the sense that, at each point, there is a CR transformation reversing the CR distribution at that point. We show that such geometries are either flat or…
We consider a complete nonnegative biminimal submanifold M (that is, a complete biminimal submanifold with lambda>=0) in a Euclidean space E^N. Assume that the immersion is proper, that is, the preimage of every compact set in E^N is also…
We conjecture an embedding operator which assigns, to any 2n+1 hermitian matrices, a 2n-dimensional hypersurface in flat (2n + 1)-dimensional Euclidean space. This corresponds to precisely defining a fuzzy D(2n)-brane corresponding to N…
We isolate a class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. This is equivalent to the nontriviality of the Brauer class of the even Clifford algebra…
In this paper we prove that a certain class of embedded unknotted curves in $\mathbb{R}^3$ evolving under curve shortening flow do not form singularities Type II before collapsing to a point. Our proof uses tools of the minimal surface…
Let $M^d$ be the spherical, Euclidean, or hyperbolic space of dimension $d\ge n+1$. Given any degenerate $(n+1)$-simplex $\mathbf{A}$ in $M^d$ with non-degenerate $n$-faces $F_i$, there is a natural partition of the set of $n$-faces into…
It is known that the properties of almost all points of R^n being not very well (multiplicatively) approximable are inherited by nondegenerate in R^n (read: not contained in a proper affine subspace) smooth submanifolds. In this paper we…
We consider the $(p+2)$-dimensional gauged supergravities arising as a consistent truncation of type II on $S^{8-p}$, which are associated with the near-horizon limit of D$p$-branes, for $p=2,4,5,6$ (and NS5-branes for $p=5$). In a…
We do not find any AdS_2 branes, neither in the H_3^+ WZNW model nor the SL(2,R) WZNW model. We then reexamine the case of the branes that possess a su(2) symmetry: we speculate that they would have to live on the boundary of AdS_3. This…
In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bezier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a…
We give an elementary proof of a compact embedding theorem in abstract Sobolev spaces. The result is first presented in a general context and later specialized to the case of degenerate Sobolev spaces defined with respect to nonnegative…
We introduce a third-order differential condition, analogous to nonzero torsion of a curve, which guarantees a submanifold of Euclidean space is totally skew in a small neighborhood. This condition is used to construct improved totally skew…
We consider the Neumann Laplacian acting on square-integrable functions on a triangle in the hyperbolic plane that has one cusp. We show that the generic such triangle has no eigenvalues embedded in its continuous spectrum. To prove this…
We show that in every commensurability class of cusped arithmetic hyperbolic manifolds of simplest type of dimension $2n+2\geq 6$ there are manifolds $M$ such that the Stiefel-Whitney classes $w_{2j}(M)$ are non-vanishing for all $0 \leq 2j…
We investigate non-abelian branes in curved space. We discuss solutions to the equations of motion of the transverse scalars when they are constant along the world-volume directions and obey an $\mathfrak{su}(2)$ or an…
The Higgs sector of the low-energy physics of n of coincident D-branes contains the necessary elements for constructing noncommutative manifolds. The coordinates orthogonal to the coincident branes, as well as their conjugate momenta, take…
Let V be a rank N vector bundle on a d-dimensional complex projective scheme X; assume that V is equipped with a skew-symmetric bilinear form with values in a line bundle L and that \Lambda^2 V^* \otimes L is ample. Suppose that the maximum…
We study spacetime singularities in a general five-dimensional braneworld with curved branes satisfying four-dimensional maximal symmetry. The bulk is supported by an analog of perfect fluid with the time replaced by the extra coordinate.…
In this paper, we construct an immersed, non-embedded $S^{n}$ $\lambda$-hypersurface in Euclidean spaces $\mathbb{R}^{n+1}$.