We consider the problem of prescribing conformally scalar curvature on compact manifolds positive Yamabe class in dimension . prove new existence results using Morse theory and some analysis blowing-up solutions under suitable pinching conditions function. also provide nonexistence showing sharpness our assumptions, both terms structure prescribed © 2021 Wiley Periodicals LLC.

Abstract Let $$\varvec{F}_q$$ F q be the finite field of q elements, where $$q=p^r$$ = p r is a power prime p , and $$\left( \beta _1, _2, \dots _r \right) $$ ...

The non-repetitive complexity function of an infinite word x (first defined by Moothathu) is the function of n that counts the number of distinct factors of length n that appear at the beginning of x prior to the first repetition of a length-n factor. We examine general properties of the non-repetitive complexity function, as well as obtain formulas for the non-repetitive complexity of the Thue...

We prove that for every three dimensional manifold with nonnegative Ricci curvature and strictly mean convex boundary (non-empty), there exists a Morse function so each connected component of its level sets has uniform diameter bound, which depends only on the lower bound curvature. This gives an upper Uryson 1-width those manifolds boundary.

Abstract We show that Gromov’s monsters arising from i.i.d. random labellings of expanders (that we call monsters) have linear divergence along a subsequence, so in particular they do not contain Morse quasigeodesics, and are quasi-isometric to graphical small cancellation expanders. Moreover, by further studying the function, there uncountably many quasi-isometry classes monsters.