We consider the problem of prescribing Gaussian and geodesic curvatures a compact surface with boundary by conformal deformation metric. derive some existence results using variational approach, either minimization Euler-Lagrange energy or via min-max methods. One main tools in our approach is blow-up analysis solutions, which present setting can have diverging volume. To knowledge, this first ...

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in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

In this paper we give a classification of simple stable singularities of Lagrange projections of the first open Whitney umbrella, the simplest singularity of Lagrange varieties. Our classification extends the ADE-classification, due to Arnold, of simple stable singularities of Lagrange projections of smooth Lagrange submanifolds. We also prove a criterion of equivalence of stable Lagrange proje...

The usual equivalence between the Palatini and metric (or affinity and vielbein) formulations of Einstein theory fails in two spacetime dimensions for its " Kaluza–Klein " reduced (as well as for its standard) version. Among the differences is the necessary vanishing of the cosmological constant in the first order forms. The purely affine Eddington formulation of Einstein theory also fails here...