Prakhar Gupta

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math.DG2024

Finite Energy Geodesic Rays in Big Cohomology Classes

Prakhar Gupta

For a big class represented by $θ$ , we show that the metric space $(E^{p} (X, θ), d_{p})$ for $p \geq 1$ is Buseman convex. This allows us to construct a chordal metric $d_{…

math.DG2024

Complete Geodesic Metrics in Big Classes

Prakhar Gupta

Let $(X, ω)$ be a compact Kähler manifold and $θ$ be a smooth closed real $(1, 1)$ -form that represents a big cohomology class. In this paper, we show that for $p \geq 1$ , the high en…