Related papers: Notes in the isometric deformations problem in cod…
In this paper, we investigate the rigidity problems of complete hypersurfaces with constant mean curvature and constant scalar curvature in Euclidean spaces. Firstly, under some conditions of Gaussian-Kronecker curvature, we provide…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
We provide a local classification of isometric immersions $f\colon L^p\times_\rho M^n\to\Q_c^{p+n+k}$ in codimensions $k=1, 2$ of warped products of Riemannian manifolds into space forms, under the assumptions that $n\geq k+1$ and that…
Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.
For real projective spaces, (a) the Euclidean immersion dimension, (b) the existence of axial maps, and (c) the topological complexity are known to be three facets of the same problem. But when it comes to embedding dimension, the classical…
This is the sequel to our first paper concerning the balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. We prove the uniqueness of such an embedding. The proof relies on fine estimates of the…
We address the problem of giving necessary and sufficient conditions in order to have robustly transitive endomorphisms admitting persistent critical sets. We exhibit different type of open examples of robustly transitive maps in any…
Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance…
The isomonodromy deformation method is applied to the scaling limits in the linear NxN matrix equations with rational coefficients to obtain the deformation equations for the algebraic curves which describe the local behavior of the reduced…
Consider a finite dimensional real vector space and a finite group acting unitarily on it. We study the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our embedding is based on subsets of sorted…
This is the second article of a sequence of research on deformations of Q-curvature. In the previous one, we studied local stability and rigidity phenomena of Q-curvature. In this article, we mainly investigate the volume comparison with…
When one applies a type of non-Hermitian effect, constant imaginary vector potential, to disordered systems, delocalization is induced even in two or lower dimension. By using the non-Hermitian induced transition as a probe, We propose a…
We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, gives explicit examples of ergodic $\mathbb{R}$-extensions of minimal…
A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main result characterizes C-rigid complexes. Specialized to the case when C is the relative…
We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…
We study the isoperimetric problem in product spaces equipped with the uniform distance. Our main result is a characterization of isoperimetric inequalities which, when satisfied on a space, are still valid for the product spaces, up a to a…
In this paper we consider the Muskat problem describing the motion of two unbounded immiscible fluid layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first prove that the mathematical model can be…
In this paper, we investigate the local-in-time well-posedness for the two-dimensional Prandtl equations in weighted Sobolev spaces under the Oleinik's monotonicity condition.Due to the loss of tangential derivative caused by vertical…
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…
We introduce two invariants called the secondary cuspidal curvature and the bias on $5/2$-cuspidal edges, and investigate their basic properties. While the secondary cuspidal curvature is an analog of the cuspidal curvature of (ordinary)…