We show the noninheritance of completeness noncompact Yamabe flow. Our main theorem states existence a long time solution which is complete for each and converges to an incomplete Riemannian metric. This shows occurrence infinite-time incompleteness.

For a domain $G$ in the one-point compactification $\overline{\mathbb{R}}^n = \mathbb{R}^n \cup \{ \infty\}$ of $\mathbb{R}^n, n \ge 2$, we characterize completeness modulus metric $\mu_G$ terms potential-theoretic thickness condition $\partial G\,,$ Martio's $M$-condition. Next, prove that G$ is uniformly perfect if and only admits minorant M\"obius invariant metric. Several applications to qu...

This paper explores the connection between fractal geometry and topological modal logic. In the early 1940’s, Tarski showed that the modal logic S4 can be interpreted in topological spaces. Since then, many interesting completeness results in the topological semantics have come to light, and renewed interest in this semantics can be seen in such recent papers as [1], [2], [3], [4], and [7]. In ...

In this paper, we shall study differential geometric properties of bounded domains in Cn. Here is the summary of our results. We consider an w-dimensional complex manifold M and the Hilbert space of square integrable holomorphic re-forms on M. After Bergman [3; 4; 5], we define the kernel form on M (instead of the kernel function) and, under certain assumptions, we define the invariant metric o...

In this paper we first study some global properties of the energy functional on a nonreversible Finsler manifold. In particular we present a fully detailed proof of the Palais–Smale condition under the completeness of the Finsler metric. Moreover we define a Finsler metric of Randers type, which we call Fermat metric, associated to a conformally standard stationary spacetime. We shall study the...

We introduce the notion of λ-spaces which is much weaker than cone metric spaces defined by Huang and X. Zhang 2007 . We establish some critical point theorems in the setting of λ-spaces and, in particular, in the setting of complete cone metric spaces. Our results generalize the critical point theorem proposed by Dancs et al. 1983 and the results given by Khanh and Quy 2010 to λ-spaces and con...

We develop the calculation of divergent part one-loop covariant effective action for scalar fields minimally and non-minimally coupled to gravity using generalized Schwinger-DeWitt technique. derive field-space metric Vilkovisky's prescription obtain new terms in corrections which are absent past literature with trivial choices metric. further calculate versions results, obtained standard appro...

In the topological semantics for modal logic, S4 is well-known to be complete wrt the rational line and wrt the real line: these are special cases of S4’s completeness wrt any dense-in-itself metric space. The construction used to prove completeness can be slightly amended to show that S4 is not only complete, but strongly complete, wrt the rational line. But no similarly easy amendment is avai...