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In this talk we show that bounded harmonic functions are constant on gradient shrinking Ricci solitons with CSC by frequency function method. As an application, we show that the space of harmonic func...
The motivation to study manifolds with scalar curvature bounded from below comes from Mathematical General Relativity and Riemannian Geometry. In this talk, I'll first briefly introduce some problems ...
In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a pro...
The Lichnerowicz formula yields an index theoretic obstruction to positive scalar curvature metrics on closed spin manifolds. The most general form of this obstruction is due to Rosenberg and takes va...
The holomorphic invariants introduced by Futaki as obstruction to the asymptotic Chow semistability are studied by an algebraic-geometric point of view and are shown to be the Mumford weights of suit...
In [7], a notion of constant scalar curvature metrics on piecewise at manifolds is de ned. Such metrics are candidates for canonical metrics on discrete manifolds. In this paper, we de ne a class of v...
In this paper, we give a characterization of tori $S^1\left(\sqrt{\frac{nr+2-n}{nr}}\right)\times S^{n-1}\left(\sqrt{\frac{n-2}{nr}}\right)$ and $S^m\left(\sqrt{\frac{m}{n}}\right)\times S^{n-m}\left(...

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