Alessandra Pluda
Schedule - Titles and Abstracts
15 December 2025 - 19 December 2025
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Closing event of the Project BIHO-NewS
BIHO - NewS
Monday 15 December
Aula Riunioni - 10:00
Stefano Borghini (Università di Napoli Federico II)
"On the mass of initial data with positive cosmological constant"
Abstract: The definition of a suitable notion of mass for time-symmetric initial data with positive cosmological constant presents a distinct challenge: the renowned counterexamples to the Min-Oo conjecture by Brendle, Marques, and Neves highlight that even the rigidity statement in a potential positive mass theorem has not been correctly identified yet in this context. We will discuss an approach to overcome this issue, leading to insights on a new notion of mass and to a characterization of the de Sitter spacetime. This is a joint work with Virginia Agostiniani and Lorenzo Mazzieri.
Aula Riunioni - 14:30
Ariadna León Quirós (Universität Tübingen)
"Vector field approach to proving the Riemannian Positive Mass Theorem"
Abstract: In 1977, D. C. Robinson developed a method for proving static vacuum Black Hole uniqueness in General Relativity. This method has recently been generalized to higher dimensions by C. Cederbaum, A. Cogo, B. Leandro, and J. Paolo dos Santos. It turns out that the same philosophy can prove several geometric inequalities.
In my talk, I will show how to adjust this approach to prove the Riemannian Positive Mass Theorem. If time permits, I will discuss other related results. This is joint work with C. Cederbaum and B. Meco.
Tuesday 16 December
Aula Riunioni - 10:00
Ivan Yuri Violo (Università di Pisa)
"Regularity of quasilinear elliptic equations in metric spaces via Galerkin method"
Abstract: The analysis of elliptic partial differential equations on metric spaces has attracted increasing attention over the last two decades. A central problem is the regularity of weak solutions. In this talk, I will show that, assuming a lower Ricci curvature bound on the ambient space in a weak sense, it is possible to obtain both Lipschitz and second-order regularity for a general class of quasilinear elliptic equations. The result is obtained using a Galerkin-type approximation method.
Joint work with S. Schulz.
Aula Riunioni - 14:30
Giorgio Gatti (Università di Padova)
"The Inverse Mean Curvature Flow in C0 Riemannian Manifolds"
Abstract: The aim of this talk is to prove existence of proper solutions for a suitable weak notion of Inverse Mean Curvature Flow in smooth manifolds equipped with a continuous Riemannian metric.
The main novelty in our approach to existence consists in combining a reverse isoperimetric inequality for the level sets of the IMCF and a Harnack type inequality to obtain local L^infinity bounds on a solution to the classical weak IMCF. These bounds are stable for sequences of solutions to the weak IMCF with respect to smooth metrics converging uniformly to a continuous metric, so they allow us to adapt to our setting a compactness scheme already present in the literature.
Wednesday 17 December
Aula Riunioni - 10:00
Mattia Fogagnolo (Università di Padova)
"Detecting scalar curvature bounds"
Abstract: I'll discuss some inequalities holding true along the level sets of the inverse mean curvature flow and related equations in 3-manifolds with nonnegative scalar curvature. Then, reversing the point of view, I'll discuss whether the validity of such inequalities could in fact characterize nonnegative scalar curvature.
Thursday 18 December
Aula Riunioni - 10:00
Marco Pozzetta (Politecnico di Milano)
"On geometric applications of prescribed mean curvature problems"
Abstract: The talk is meant to be an introductory lecture on topological and geometric applications of prescribed mean curvature problems in Riemannian geometry. We will survey some classical and recent results on topological or geometric rigidities for manifolds with nonnegative curvature, discussing proofs that rely on the analysis of surfaces that minimize suitable functionals given by a volume perturbation of the area, i.e., minimizers to prescribed mean curvature problems. We will also discuss open applications and problems.
Aula Riunioni - 14:30
Alessandra Pluda (Università di Pisa)
"Minimal and Evolving Networks"
Abstract: For the past ten years, my research has been primarily focused on the study of minimal networks - finite unions of sufficiently smooth curves whose endpoints meet at junctions - from both a static and dynamic perspective.
I have primarily studied two topics: the network Flow and the Steiner Problem.
The network Flow is a generalization of the Curve Shortening Flow (CSF) . The CSF is an evolution equation in which a curve evolves with normal velocity equal to its curvature; it can be understood as the gradient flow of the length functional.
The Steiner Problem, in its classical formulation, is to find the 1-dimensional connected set in the plane with the minimal length that contains a finite collection of given points .
In this talk, I will summarize my work on these two subjects and describe the current open problems in the field.
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