In this paper, we introduce a potential theory for the k-curvature equation, which can also be seen as a PDE approach to curvature measures. We assign a measure to a bounded, upper semicontinuous function which is strictly subharmonic with respect to the k-curvature operator, and establish the weak continuity of the measure
The curvature tensor measures the extent to which covariant differentiation on manifolds differs fro...
The curvature tensor measures the extent to which covariant differentiation on manifolds differs fro...
We study the existence of subharmonic solutions of the prescribed curvature equation . According to ...
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mea...
We show that the tools recently introduced by the first author in [9] allow to give a PDE descriptio...
Abstract. In this paper we survey some recent results in connection with the so called Painlevé’s p...
This thesis consists of two parts: In part I we apply the statistical mechanics techniques to a ge...
We analyze the lower semicontinuous envelope of the curvature functional of Cartesian surfaces in co...
Partial differential equations (PDEs) and geometric measure theory (GMT) are branches of analysis wh...
We establish the convexity of Mabuchi’s K-energy functional along weak geodesics in the space of K\u...
We prove that any Kantorovich potential for the distance-squared cost function on a Riemannian manif...
Potential Theory presents a clear path from calculus to classical potential theory and beyond, with ...
We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, ...
We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, ...
This thesis consists of two parts: In part I we apply the statistical mechanics tech-niques to a gen...
The curvature tensor measures the extent to which covariant differentiation on manifolds differs fro...
The curvature tensor measures the extent to which covariant differentiation on manifolds differs fro...
We study the existence of subharmonic solutions of the prescribed curvature equation . According to ...
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mea...
We show that the tools recently introduced by the first author in [9] allow to give a PDE descriptio...
Abstract. In this paper we survey some recent results in connection with the so called Painlevé’s p...
This thesis consists of two parts: In part I we apply the statistical mechanics techniques to a ge...
We analyze the lower semicontinuous envelope of the curvature functional of Cartesian surfaces in co...
Partial differential equations (PDEs) and geometric measure theory (GMT) are branches of analysis wh...
We establish the convexity of Mabuchi’s K-energy functional along weak geodesics in the space of K\u...
We prove that any Kantorovich potential for the distance-squared cost function on a Riemannian manif...
Potential Theory presents a clear path from calculus to classical potential theory and beyond, with ...
We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, ...
We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, ...
This thesis consists of two parts: In part I we apply the statistical mechanics tech-niques to a gen...
The curvature tensor measures the extent to which covariant differentiation on manifolds differs fro...
The curvature tensor measures the extent to which covariant differentiation on manifolds differs fro...
We study the existence of subharmonic solutions of the prescribed curvature equation . According to ...
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