Titlebook: New Trends in Geometric Analysis; Spanish Network of G Antonio Alarcón,Vicente Palmer,César Rosales Book 2023 The Editor(s) (if applicable)

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https://doi.org/10.1007/978-3-031-39916-9Geometric Analysis; Riemannian Geometry; Convex Geometry; Sub-Riemannian Geometry; Mean Curvature Flow; G

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978-3-031-39918-3The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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New Trends in Geometric Analysis978-3-031-39916-9Series ISSN 2509-8888 Series E-ISSN 2509-8896

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Snapshots of Non-local Constrained Mean Curvature-Type Flows, In 1987, G. Huisken (J. Reine Angew. Math. 382:35–48 (1987)) introduced a variant that keeps the enclosed volume constant while the area decreases. For this modification, a global term is added to the speed of the original flow, which makes the usual methods in geometric flows (e.g. maximum princip

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Conjugate Plateau Constructions in Product Spaces,aces immersed in homogeneous Riemannian three-manifolds with isometry group of dimension four. On the one hand, we collect the results and strategies in the literature that have been developed so far to deal with the analysis of conjugate surfaces and their embeddedness. On the other hand, we revisi

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Homogeneous Hypersurfaces in Symmetric Spaces,ces have remarkable geometric properties, providing the simplest examples of hypersurfaces with constant mean curvature. Thus, they are crucial for the investigation of more general types of submanifolds in ambient spaces with large isometry groups..In this survey article, we present an introduction