Related papers: A rigidity theorem on the second fundamental form …
In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More precisely, we show that every minimal non-degenerate critical…
Suppose $(M^n, g, f)$ is a complete shrinking gradient Ricci soliton. We give several rigidity results under some natural conditions, generalizing the results in \cite{Petersen-Wylie,Guan-Lu-Xu}. Using maximum principle, we prove that…
We take advantage of a rigidity result for the equation satisfied by an extremal function associated with a special case of the Caffarelli-Kohn-Nirenberg inequalities to get a symmetry result for a larger set of inequali-ties. The main…
In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…
It is our purpose to study complete self-shrinkers in Euclidean space. First of all, we show some examples of complete self-shrinkers without polynomial volume growth. By making use of the generalized maximum principle for…
In this paper, we study the rigidity of eigenvalues of shring Ricci solitons. It is known that the drifted Laplacian on shrinking Ricci solitons has discrete spectrum, its eigenvalues have a lower bound and a rigidity result holds. Firstly,…
We show that the problem `whether a finite set of regular-linear axioms defines a rigid theory' is undecidable.
We prove local versions of the Ricci curvature and $\nu$-entropy gap theorems for Ricci shrinkers, which respectively generalize a previous result of Munteanu-Wang and a prior result of the authors with Ma. The key point is that these local…
We extend Wilkes' results on the profinite rigidity of SFSs to the setting of central extensions of 2-orbifold groups with higher-rank centre. We prove that both rigid and non-rigid phenomena arise in this setting and that the non-rigid…
In this paper, we study the rigidity problem for compact minimal Legendrian submanifolds in the unit Euclidean spheres via eigenvalues of fundamental matrices, which measure the squared norms of the second fundamental form on all normal…
In this note we generalize the Ball-James rigidity theorem for gradient differential inclusions to the setting of a general linear differential constraint. In particular, we prove the rigidity for approximate solutions to the two-state…
Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First, we provide a complete description of the Weyl tensor for…
In this paper, we proved a rigidity theorem of the Hodge metric for concave horizontal slices and a local rigidity theorem for the monodromy representation.
By iterative techniques,we present two fixed point theorems, whose modular formulations are relatively close to the Banach's fixed point theorem in the normed spaces.The first result concerns the fixed point of the strongly contraction…
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…
We consider a perturbation $f$ of a hyperbolic toral automorphism $L$. We study rigidity related to exceptional properties of the strong and weak stable foliations for $f$. If the strong foliation is mapped to the linear one by the…
We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…
We prove rigidity type results on the vanishing of stable (co)homology for modules of finite complete intersection dimension, results which generalize and improve upon known results. We also introduce a notion of pre-rigidity, which…