arXiv research

In this paper, we discuss a rigidity property for holomorphic disks in Teichmüller space. In fact, we give a refinement of Tanigawa's rigidity theorem. We will also treat the rigidity property of holomorphic disks for complex manifolds. We observe the rigidity property is valid for bounded strictly pseudoconvex domains…

Discussing rigidity properties of conics, inspired by billiards in ellipses.

Let $Γ$ be a discrete group with property $(T)$ of Kazhdan. We prove that any Riemannian isometric action of $Γ$ on a compact manifold $X$ is locally rigid. We also prove a more general foliated version of this result. The foliated result is used in our proof of local rigidity for standard actions of higher rank semisi…

Study geometric rigidity of surfaces in negative curvature manifolds.

Study on finiteness properties of handlebody mapping class groups.

In this article, we survey recent developments in defining the quasi-local mass in general relativity. We discuss various approaches and the properties and applications of the different definitions. Among the expected properties, we focus on the rigidity property: for a surface in the Minkowski spacetime, one expects t…

The paper proves rigidity of certain Dirac operators using theta functions.

Examines how irreducibility and rigidity affect digital images.

Proves rigidity of sphere metrics with subsets removed.

Study Busemann spaces with measures under MCP, proving rigidity and structure theorems.

The paper develops techniques to study dynamical systems with Carnot metrics.

Study shows rigidity for entropy minimizers in non-monotone cases.

We give rigidity results for the discrete Bonnet-Myers diameter bound and the Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a hypercube. The proofs use well-known semigroup methods as well as new direct methods which translate curvature to combinatorial properties.…

Graphically discrete groups have strong rigidity properties.

We study the rigidity results for self-shrinkers in Euclidean space by restriction of the image under the Gauss map. The geometric properties of the target manifolds carry into effect. In the self-shrinking hypersurface situation Theorem 3.1 and Theorem 3.2 not only improve the previous results, but also are optimal. I…

Projective structures are mostly rigid at the boundary but some are not.

The paper explores higher property T in lattices and its connections to geometric phenomena.

Groups with certain properties have invariant subalgebra rigidity.

The paper proves rigidity of certain solitons with specific properties.

Let $X$ and $Y$ be length metric spaces. Let $\mathcal H^n$ denote the $n$-dimensional Hausdorff measure. The Lipschitz-Volume Rigidity is a property that if there exists a 1-Lipschitz map $f\colon X\to Y$ and $0<\mathcal H^n(X)=\mathcal H^n(f(X))<\infty$, then $f$ preserves the length of path. This property holds for …

Paper shows non-arithmetic surface with unique geometric property.

The paper examines Sasaki-Ricci solitons and their transverse rigidity properties.

Discussing rigidity in codimension 2, extending rigidity concepts.

Study circumcenters in Finsler unitary groups with optimal convexity bounds.

We give a new proof that compact infra-solvmanifolds with isomorphic fundamental groups are smoothly diffeomorphic. More generally, we prove rigidity results for manifolds which are constructed using affine actions of virtually polycyclic groups on solvable Lie groups. Our results are derived from rigidity properties o…

Study geometric properties of generalized vacuum static spaces.

In this paper, we study some basic geometric properties of pseudohermitian submanifolds of the Heisenberg groups. In particular, we obtain the uniqueness and existence theorems, and some rigidity theorems.

Study simplifies homotopy groups of 6D manifolds.

The study finds monotonic properties of harmonic functions on 3-manifolds with a flat end.

H. Weyl in 1921 demonstrated that for a connected manifold of dimension greater than $1$, if two Riemannian metrics are conformal and have the same geodesics up to a reparametrization, then one metric is a constant scaling of the other one. In the present paper, we investigate the analogous property for sub-Riemannian …

Given a closed hyperbolic Riemannian surface, the aim of the present paper is to describe an explicit construction of smooth deformations of the hyperbolic metric into Finsler metrics that are not Riemannian and whose properties are such that the classical Riemannian results about entropy rigidity, marked length spectr…

The Hawking energy is nonnegative and rigid on area-constrained surfaces in general relativity.

Characterizes rigid and flexible hyperbolic cone metrics and billiards.

Study on compact biconservative hypersurfaces in de Sitter space.

Study biharmonic hypersurfaces in spheres, proving unique continuation theorem.

Paper extends rigidity and vanishing results for totally real submanifolds under $L^p$-integrable conditions.

We prove that any rigid representation of $π_1Σ_g$ in $\mathrm{Homeo}_+(S^1)$ with Euler number at least $g$ is necessarily semi-conjugate to a discrete, faithful representation into $\mathrm{PSL}(2,\mathbb{R})$. Combined with earlier work of Matsumoto, this precisely characterizes Fuchsian actions by a topological rig…

Boundary rigidity defined for hyperbolic spaces, tied to geometric properties.

Study Poisson boundaries of building lattices and generalize rigidity results.

Proves a property of certain 3D knots and links.

The paper proves rigidity and stability properties of self-shrinking surfaces in 3D space.

Abstract: Survey on quadratic Hessian equations, their properties, and open problems.

In this paper, we prove some rigidity theorems for compact Bach-flat $n$-manifold with the positive constant scalar curvature. In particular, our conditions in Theorem 1.4 have the additional properties of being sharp.

New insights into profinite rigidity of Kleinian groups and their subgroups.

New rigidity result for maps between curved spaces.

Paper proves rigidity of manifolds with specific curvature and submanifold properties.

Since $n$-dimensional $λ$-hypersurfaces in the Euclidean space $\mathbb {R}^{n+1}$ are critical points of the weighted area functional for the weighted volume-preserving variations, in this paper, we study the rigidity properties of complete $λ$-hypersurfaces. We give a gap theorem of complete $λ$-hypersurfaces with po…

Study finds rigidity of biconservative hypersurfaces in space forms without curvature assumptions.