Lemma 17.10.22`BDEA4F06B7F1`

Lemma 17.10.22.BDEA4F06B7F1 Let $\varphi _0,\varphi _1\in \mathrm{PSH}(X,\theta )$. Assume that there is a subgeodesic from $\varphi _0$ to $\varphi _1$. Then the geodesic $(\varphi _ t)_{t\in (0,1)}$ from $\varphi _0$ to $\varphi _1$ is a subgeodesic from $\varphi _0$ to $\varphi _1$.

Proof. This is an immediate consequence of proposition 17.10.13. $\square$

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@misc{pome-tag-BDEA4F06B7F1,
  author = {{Pome contributors}},
  title = {Lemma 17.10.22},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/BDEA4F06B7F1/}
}

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Lemma 17.10.22BDEA4F06B7F1

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Lemma 17.10.22`BDEA4F06B7F1`