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Median geometry for spaces with measured walls and for groups. [PDF]
Chatterji I, Druţu C.
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Energy quantization for Willmore surfaces with bounded index
Journal of the European Mathematical Society (Print), 2023We prove an energy quantization result for Willmore surfaces with bounded index, whether the underlying Riemann surfaces degenerate in the moduli space or not. To do so, we translate the question on the conformal Gauss map’s viewpoint.
Dorian Martino
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2022
Summary: The Sombor index of the graph \(G\) is a degree based topological index, defined as \(\mathrm{SO} = \sum_{uv \in \mathbf{E}(G)} \sqrt{d_u^2+d_v^2}\), where \(d_u\) is the degree of the vertex \(u\), and \(\mathbf{E}(G)\) is the edge set of \(G\).
Gutman, Ivan +3 more
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Summary: The Sombor index of the graph \(G\) is a degree based topological index, defined as \(\mathrm{SO} = \sum_{uv \in \mathbf{E}(G)} \sqrt{d_u^2+d_v^2}\), where \(d_u\) is the degree of the vertex \(u\), and \(\mathbf{E}(G)\) is the edge set of \(G\).
Gutman, Ivan +3 more
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Functions of bounded index, bounded value distribution and v-bounded index
Nonlinear Analysis: Theory, Methods & Applications, 1987If for an entire function f there exists an integer N such that for all \(z\in {\mathbb{C}}\) and \(k\in {\mathbb{N}}\) \[ \max_{0\leq j\leq N}\{| f^{(j)}(z)| /j!\}\geq | f^{(k)}(z)| /k!, \] then f is called of bounded index and the least number N is called the ``index'' of f.
Roy, Ranjan, Shah, S. M.
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Derivations and bounded nilpotence index
International Journal of Algebra and Computation, 2015We construct a nil ring R which has bounded index of nilpotence 2, is Wedderburn radical, and is commutative, and which also has a derivation δ for which the differential polynomial ring R[x;δ] is not even prime radical. This example gives a strong barrier to lifting certain radical properties from rings to differential polynomial rings.
Nielsen, Pace P., Ziembowski, Michał
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A note on minimal surfaces with bounded index
Communications in analysis and geometry, 2018For any closed Riemannian three-manifold, we prove that for any sequence of closed embedded minimal surfaces with uniformly bounded index, the genus can only grow at most linearly with respect to the area.
Davi Máximo
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