Abstract We show a kind of Obata-type theorem on compact Einstein n -manifold $$(W, \bar{g})$$ ( W , g ¯ ) with smooth boundary $$\partial W$$ ∂ . Assume that t...

We prove a CR version of the Obata’s result for the first eigenvalue of the sub-Laplacian in the setting of a compact strictly pseudoconvex pseudohermitian three dimensional manifold with non-negative CR-Paneitz operator which satisfies a Lichnerowicz type condition. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of t...

Persistent truncus arteriosus is characterized by a single arterial trunk arising from the heart and supplying the systemic, pulmonary, and coronary circulations. There are remnants neither of an atretic pulmonary artery nor aorta (Lev and Saphir, 1942; Collett and Edwards, 1949). Despite excellent clinical reviews (Anderson, Obata, and Lillehei, 1957; Tandon, Hauck, and Nadas, 1963; McCue et a...

there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

Through the work of Obata [25], Gidas-Ni-Nirenberg [10] and Caffarelli-GidasSpruck [6], the asymptotic behavior of solutions of (1.1) as well as the classification of global solutions are well understood in the case when c = 0. In [28] Véron raised the following question: For c ∈ R, c 6= 0 and n ≥ 3, let u ∈ C∞(Rn\{0}) satisfy (1.1). Is it true that u must be radially symmetric about the origin...

The concept of a locally compact hypergroup was introduced by Dunkl [6], Jewett [14] and Spector [26]. Hypergroups generalize convolution algebras of measures associated to groups as well as linearization formulae of classical families of special functions, e.g. orthogonal polynomials. Many results of harmonic analysis on locally compact abelian groups can be carried over to the case of commuta...

Persistent truncus arteriosus is characterized by a single arterial trunk arising from the heart and supplying the systemic, pulmonary, and coronary circulations. There are remnants neither of an atretic pulmonary artery nor aorta (Lev and Saphir, 1942; Collett and Edwards, 1949). Despite excellent clinical reviews (Anderson, Obata, and Lillehei, 1957; Tandon, Hauck, and Nadas, 1963; McCue et a...