相关论文: Universal spaces for manifolds equipped with a clo…

It is conjectured since long that for any convex body $K \subset \mathbb{R}^n$ there exists a point in the interior of $K$ which belongs to at least $2n$ normals from different points on the boundary of $K$. The conjecture is known to be…

We decompose the twisted index obstruction $\theta(M)$ against positive scalar curvature metrics for oriented manifolds with spin universal cover into a pairing of a twisted $K$-homology with a twisted $K$-theory class and prove that…

We improve the bound on K\"uhnel's problem to determine the smallest $n$ such that the $k$-skeleton of an $n$-simplex $\Delta_n^{(k)}$ does not embed into a compact PL $2k$-manifold $M$ by showing that if $\Delta_n^{(k)}$ embeds into $M$,…

Let $M$ be a compact Riemannian manifold not containing any totally geodesic surface. Our main result shows that then the area of any complete surface immersed into $M$ is bounded by a multiple of its extrinsic curvature energy, i.e. by a…

We use a new method to give conditions for the existence of a local isometric immersion of a Riemannian $n$-manifold $M$ in $\mathbb{R}^{n+k}$, for a given $n$ and $k$. These equate to the (local) existence of a $k$-tuple of scalar fields…

We introduce the concept of $k-$future convex spacelike/null hypersurface $\Sigma$ in an $n+1$ dimensional spacetime $M$ and prove that no $k-$dimensional closed trapped submanifold (k-CTM) can be tangent to $\Sigma$ from its future side.…

In this paper, a generalized cusp is a properly convex manifold with strictly convex boundary that is diffeomorphic to $M \times [0, \infty)$ where $M$ is a closed Euclidean manifold. These are classified in [2]. The marked moduli space is…

We show that if a compact, connected, and oriented $n$-manifold $M$ without boundary admits a non-constant non-injective uniformly quasiregular self-map, then the dimension of the real singular cohomology ring $H^*(M; \mathbb{R})$ of $M$ is…

A relevant property of equifocal submanifolds is that their parallel sets are still immersed submanifolds, which makes them a natural generalization of the so-called isoparametric submanifolds. In this paper, we prove that the regular…

We consider open, oriented 3-manifolds which are infinite connected sums of closed 3-manifolds. We introduce some topological invariants for these manifolds and obtain a classification in the case where there are only finitely many summands…

Let $M$ be a complete hyperbolic $n$-manifold, $n\geq 2$. Via integration over geodesic simplices, any closed bounded differential 2-form on $M$ defines a bounded cohomology class in $H^2_b(M)$. It was proved by Barge and Ghys (for $n=2$)…

In this paper, for an immersion $f$ of an $n$-dimensional Riemannian manifold $M$ into $(n+d)$-Euclidean space we give a sufficient condition on $f$ so that, in case $d\leq 5$, any immersion $g$ of $M$ into $(n+d+1)$-Euclidean space that…

We give a curvature dependent lower bound for the filling radius of all closed Riemannian manifolds as well as an upper one for manifolds which are the total space of a Riemannian submersion. The latter applies also to the case of…

In this paper, we prove that there exists a universal constant $C$, depending only on positive integers $n\geq 3$ and $p\leq n-1$, such that if $M^n$ is a compact free boundary submanifold of dimension $n$ immersed in the Euclidean unit…

We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold…

A cusp-decomposable manifold is a manifold constructed from a finite number of complete, negatively curved, finite volume manifolds and identifying the boundaries of truncated cusps by diffeomorphisms. Using properties of the electric space…

We consider embeddings of 3-manifolds in $S^4$ such that each of the two complementary regions has an abelian fundamental group. In particular, we show that an homology handle $M$ has such an embedding if and only if $\pi_1(M)'$ is perfect,…

For each composite number $n\ne 2^k$, there does not exist a single connected closed $(n+1)$-manifold such that any smooth, simply-connected, closed $n$-manifold can be topologically flat embedded into it. There is a single connected closed…

The structure space S(M) of a closed topological m-manifold M classifies bundles whose fibers are closed m-manifolds equipped with a homotopy equivalence to M. We construct a highly connected map from S(M) to a concoction of algebraic…

We prove a conjecture of Odaka--Oshima, which says that there is an algebraic description of the Gromov--Hausdorff compactification of all unit-diameter hyperk\"ahler metrics on K3 surfaces. As a corollary, we obtain a classification of the…