Examples of scalar-flat hypersurfaces in Rn+1\mathbb{R}^{n+1}

Given a hypersurface $M$ of null scalar curvature in the unit sphere $\mathbb{S}^n$, $n\ge 4$, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in \Rr^{n+1} as a normal graph over a truncated cone generated by $M$. Furthermore, this graph is 1-stable if the cone is strictly 1-stable.Comment: Paper accepted to publication in Manuscripta Mathematic

The Dirichlet Problem for Curvature Equations in Riemannian Manifolds

We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allows us to extend some of the existence theorems of Caffarelli, Nirenberg and Spruck [4] and Ivochkina, Trundinger and Lin [19] to more general curvature functions and less convex domains.Comment: 32 pages, no figures. Final version. Paper accepted to publication in Indiana University Mathematics Journa

CHARISMATIC LEADERSHIP OF SCHOOL HEADS, SUPERVISORY RELATIONSHIP AND RECIPROCITY BELIEFS: PATH MODEL ON WORK ETHICS OF PUBLIC ELEMENTARY SCHOOL TEACHERS

The goal of this study was to identify the model that best match with the work ethics of public elementary school teachers as estimated by charismatic leadership, supervisory relationship and reciprocity beliefs of school heads in Region XI, Philippines. Conducted from June 2021 to November 2022 using a correlation approach and path analysis, which study employed a quantitative, non-experimental research design. A stratified sampling approach was used to determine the 432 teachers of public elementary schools. Statistics methods employed included mean, Pearson r, and path analysis. Moreover, adapted survey questionnaires were used. The result reveals that the levels of charismatic leadership, supervisory relationship and reciprocity beliefs of schools and work ethics of teachers were very high. Further, when each independent variable correlates with work ethics of teachers, results showed that charismatic leadership was significantly correlated with work ethics. There was also a significant relationship between supervisory relationship and work ethics as well as between reciprocity beliefs and work ethics. Model 3 came out as the best fit model that predicts work ethics. The model showed that charismatic leadership and reciprocity beliefs predicts work ethics among public school teachers.  Article visualizations