相关论文: Lemme de l'Ombre et non divergence des horosph\`er…

In this paper, we prove conformal positive mass theorems for asymptotically flat manifolds with charge. We apply conformal relations to show that if the conformal sum of scalar curvature is not less than the norm square of electric field…

Many important theorems in differential topology relate properties of manifolds to properties of their underlying homotopy types -- defined e.g. using the total singular complex or the \v{C}ech nerve of a good open cover. Upon embedding the…

In this paper, we investigate analytical and geometric properties of certain non-compact boundary-manifolds, namely manifolds of bounded geometry. One result are strong Bochner type vanishing results for the L^2-cohomology of these…

We briefly review some recent advances in the study of the shadows of rotating black holes in alternative theories. The size and the shape of the shadow depend on the mass and the angular momentum, and they can also depend on other…

We prove a splitting theorem for a smooth noncompact manifold with (possibly noncompact) boundary. We show that if a noncompact manifold of dimension $n\geq 2$ has $\lambda_1(-\alpha\Delta+\operatorname{Ric})\geq 0$ for some…

In this paper, we prove a total curvature estimate of closed hypersurfaces in simply-connected non-positively curved symmetric spaces, and as a corollary, we obtain an isoperimetric inequality for such manifolds.

A classical theorem of A.D. Alexandrov says that a connected compact smooth hypersurface in Euclidean space with constant mean curvature must be a sphere. We give exposition to some results on symmetry properties of hypersurfaces with…

We prove a finiteness theorem for the class of complete finite volume Riemannian manifolds with pinched negative sectional curvature, fixed fundamental group, and of dimension $>2$. One of the key ingredients is that the fundamental group…

We study closed orientable surfaces satisfying the spectral condition $\lambda_1(-\Delta+\beta K)\geq\lambda\geq0$, where $\beta$ is a positive constant and $K$ is the Gauss curvature. This condition naturally arises for stable minimal…

In a recent paper, the authors proved that no spin foliation on a compact enlargeable manifold with Hausdorff homotopy graph admits a metric of positive scalar curvature on its leaves. This result extends groundbreaking results of…

In this paper, we prove a dihedral extremality and rigidity theorem for a large class of codimension zero submanifolds with polyhedral boundary in warped product manifolds. We remark that the spaces considered in this paper are not…

We study a class of non-smooth asymptotically flat manifolds on which metrics fails to be $C^1$ across a hypersurface $\Sigma$. We first give an approximation scheme to mollify the metric, then we prove that the Positive Mass Theorem still…

In this work, various versions of the so-called Omega-Lemma are provided, which ensure differentiability properties of pushforwrds between spaces of C^r-sections (or compactly supported C^r-sections) in vector bundles over…

Inspired by a Blaschke's work about analytic convex surfaces, we study {\em shadow boundaries} of Riemannian submanifolds $M$, which are defined by a parallel vector field along $M$. Since a shadow boundary is just a closed subset of $M$,…

The gravitational deflection of light is a critical test of modified theories of gravity. A few years ago, Gibbons and Werner introduced a definition of the deflection angle based on the Gauss-Bonnet theorem. In more recent years, Arakida…

We prove spectral, stochastic and mean curvature estimates for complete $m$-submanifolds $\varphi \colon M \to N$ of $n$-manifolds with a pole $N$ in terms of the comparison isoperimetric ratio $I_{m}$ and the extrinsic radius…

We formulated a mirror-free approach to the mirror conjecture, namely, quantum hyperplane section conjecture, and proved it in the case of nonnegative complete intersections in homogeneous manifolds. For the proof we followed the scheme of…

We prove that a closed 4-manifold has shadow-complexity zero if and only if it is a kind of 4-dimensional graph manifold, which decomposes into some particular blocks along embedded copies of S^2 x S^1, plus some complex projective spaces.…

We conjecture that any perverse sheaf on a compact aspherical K\"ahler manifold has non-negative Euler characteristic. This extends the Singer-Hopf conjecture in the K\"ahler setting. We verify the stronger conjecture when the manifold X…

In this paper we prove that on a complete smooth metric measure space with non-negative Bakry-\'Emery-Ricci curvature if the space of weighted L^2 harmonic one-forms is non-trivial then the weighted volume of the manifold is finite and…