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Enclosure Theorems for Extremals of Elliptic Parametric Functionals
 CALC. VAR
, 2001
"... In the following paper we study parametric functionals. First we introduce a generalized mean curvature (so called Fmean curvature). This enables us to describe extremals of parametric funcionals as surfaces of prescribed Fmean curvature. Furthermore we give a differential equation for arbitrary i ..."
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In the following paper we study parametric functionals. First we introduce a generalized mean curvature (so called Fmean curvature). This enables us to describe extremals of parametric funcionals as surfaces of prescribed Fmean curvature. Furthermore we give a differential equation for arbitrary immersions generalizing #X = HN and apply this equation to surfaces of vanishing and prescribed Fmean curvature. Especially we prove nonexistence results for such surfaces generalizing Theorems by Hildebrandt and Dierkes [3], [6].
Note on a nonlinear eigenvalue problem
 Rocky Mountain J. of Math
, 1993
"... My lectures at theMinicorsi di Analisi Matematica at Padova in June ..."
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Cited by 11 (1 self)
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My lectures at theMinicorsi di Analisi Matematica at Padova in June
Elliptic approximations of prescribed mean curvature surfaces in Finsler geometry
 Asymptotic Anal
"... ..."
A SECOND EIGENVALUE BOUND FOR THE DIRICHLET LAPLACIAN IN HYPERBOLIC SPACE
, 2005
"... Abstract. Let Ω be some domain in the hyperbolic space H n (with n ≥ 2) and S1 the geodesic ball that has the same first Dirichlet eigenvalue as Ω. We prove the PaynePólyaWeinberger conjecture for H n, i.e., that the second Dirichlet eigenvalue on Ω is smaller or equal than the second Dirichlet ei ..."
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Abstract. Let Ω be some domain in the hyperbolic space H n (with n ≥ 2) and S1 the geodesic ball that has the same first Dirichlet eigenvalue as Ω. We prove the PaynePólyaWeinberger conjecture for H n, i.e., that the second Dirichlet eigenvalue on Ω is smaller or equal than the second Dirichlet eigenvalue on S1. We also prove that the ratio of the first two eigenvalues on geodesic balls is a decreasing function of the radius. 1.
Harmonic Analysis in Value at Risk Calculations
, 1996
"... . Value at Risk is a measure of risk exposure of a portfolio and is defined as the maximum possible loss in a certain time frame, typically 120 days, and within a certain confidence, typically 95%. Full valuation of a portfolio under a large number of scenarios is a lengthy process. To speed it up, ..."
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. Value at Risk is a measure of risk exposure of a portfolio and is defined as the maximum possible loss in a certain time frame, typically 120 days, and within a certain confidence, typically 95%. Full valuation of a portfolio under a large number of scenarios is a lengthy process. To speed it up, one can make use of the total delta vector and the total gamma matrix of a portfolio and compute a Gaussian integral over a region bounded by a quadric. We use methods from harmonic analysis to find approximate analytic formulas for the Value at Risk as a function of time and of the confidence level. In this framework, the calculation is reduced to the problem of evaluating linear algebra invariants such as traces of products of matrices, which arise from a Feynmann expansion. The use of Fourier transforms is crucial to resum the expansions and to obtain formulas that smoothly interpolate between low and large confidence levels, as well as between short and long time horizons. 1 email: al...
Exact mathematical models of a unified quantum theory; Static and
, 909
"... expanding micro universes ..."
Contents
, 2009
"... 2 Sequences of KählerEinstein metrics 2 2.1 Differential Geometric input..................... 3 2.2 The main argument......................... 5 ..."
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2 Sequences of KählerEinstein metrics 2 2.1 Differential Geometric input..................... 3 2.2 The main argument......................... 5
ON A N ON LIN EAR EIGEN VALUE PROBLEM
"... My lectures at the ”Minicorsi di Analisi Matematica ” at Padova in June 2000 ..."
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My lectures at the ”Minicorsi di Analisi Matematica ” at Padova in June 2000