| 1. |
- Berndtsson, Bo, 1950
(author)
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Convexity on the space of Kähler metrics
- 2013
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In: Annales de la Faculté des Sciences de Toulouse. - : Cellule MathDoc/CEDRAM. - 0240-2955 .- 0240-2963 .- 2258-7519. ; 22 (6):4, s. 713-746
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Journal article (peer-reviewed)
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| 2. |
- Berman, Robert, 1976, et al.
(author)
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Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties
- 2013
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In: Annales de la faculté des sciences de Toulouse. - : Cellule MathDoc/CEDRAM. - 0240-2963 .- 2258-7519. ; 22:4, s. 649-711
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Journal article (peer-reviewed)abstract
- We show, using a direct variational approach, that the second boundary value problem for the Monge-Ampère equation in $\mathbb{R}^{n}$ with exponential non-linearity and target a convex body $P$ is solvable iff $0$ is the barycenter of $P.$ Combined with some toric geometry this confirms, in particular, the (generalized) Yau-Tian-Donaldson conjecture for toric log Fano varieties $(X,\Delta )$ saying that $(X,\Delta )$ admits a (singular) Kähler-Einstein metric iff it is K-stable in the algebro-geometric sense. We thus obtain a new proof and extend to the log Fano setting the seminal result of Wang-Zhou concerning the case when $X$ is smooth and $\Delta $ is trivial. Li’s toric formula for the greatest lower bound on the Ricci curvature is also generalized. More generally, we obtain Kähler-Ricci solitons on any log Fano variety and show that they appear as the large time limit of the Kähler-Ricci flow. Furthermore, using duality, we also confirm a conjecture of Donaldson concerning solutions to Abreu’s boundary value problem on the convex body $P$ in the case of a given canonical measure on the boundary of $P.$
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| 3. |
- Brenner, Philip, 1941, et al.
(author)
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Nonlinear Maps between Besov and Sobolev spaces
- 2010
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In: Annales de la Faculte des Sciences de Toulouse. - : Cellule MathDoc/CEDRAM. - 0240-2963 .- 2258-7519. ; 19:1, s. 105-120
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Journal article (other academic/artistic)abstract
- Our main result shows that for a large class of nonlinear local mappings between Besov and Sobolev space, interpolation is an exceptional low dimensional phenomenon. This extends previous results by Kumlin [13] from the case of analytic mappings to Lipschitz and Hölder continuous maps (Corollaries 1 and 2), and which go back to ideas of the late B.E.J. Dahlberg [8].
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| 4. |
- Sznajdman, Jacob, 1983
(author)
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An elementary proof of the Briancon-Skoda theorem
- 2010
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In: Ann. fac. sci. Toulouse. - : Cellule MathDoc/CEDRAM. - 0240-2963. ; Ser. 6, Vol. 19:3-4
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Journal article (peer-reviewed)abstract
- We give an elementary proof of the Briancon-Skoda theorem. The theorem gives a criterion for when a function \phi belongs to an ideal I of the ring of germs of analytic functions at 0 \in ℂ^n; more precisely, the ideal membership is obtained if a function associated with \phi and I is locally square integrable. If I can be generated by m elements, it follows in particular that the integral closure of I^min(m,n) is contained in I.
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| 5. |
- Andersson, Mats, 1957
(author)
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The flatness of the $\mathcal O$-module of smooth functions and integral representation
- 2022
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In: Annales de la Faculté des Sciences de Toulouse. - 2258-7519. ; In press
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Journal article (peer-reviewed)abstract
- We give a proof of the well-known fact that the $\Ok$-module $\E$ of smooth functions is flat by means of residue theory and integral formulas. A variant of the proof gives a related statement for classes of functions of lower regularity. We also prove a Brian\c con-Skoda type theorem for ideals of the form $\E a$, where $a$ is an ideal in $\Ok$.
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| 6. |
- Borell, Christer, 1945
(author)
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Minkowski sums and Brownian exit times
- 2007
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In: ANNALES DE LA FACULTE DES SCIENCES DE TOULOUSE Mathematiques. - 0240-2963. ; XVI:1, s. 37-47
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Journal article (peer-reviewed)abstract
- If C is a domain in R^n, the Brownian exit time of C is denoted by T^C. Given domains C and D in R^n this paper gives an upper bound of the distribution function of T^(C+D) when the distribution functions of T^C and T^D are known. The bound is sharp if C and D are parallel affine half-spaces. The paper also exhibits an extension of the Ehrhard inequality.
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| 7. |
- Kiselman, Christer O., 1939-
(author)
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Analytic continuation of fundamental solutions to differential equations with constant coefficients
- 2011
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In: Annales de la Faculté des Sciences de Toulouse, Mathématiques. - Toulouse : Université Paul Sabatier. - 0240-2963. ; (6) 20:S2, s. 153-182
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Journal article (peer-reviewed)abstract
- If $P$ is a polynomial in ${\bf R}^n$ such that $1/P$ integrable, then the inverse Fourier transform of $1/P$ is a fundamental solution $E_P$ to the differential operator $P(D)$. The purpose of the article is to study the dependence of this fundamental solution on the polynomial $P$. For $n=1$ it is shown that $E_P$ can be analytically continued to a Riemann space over the set of all polynomials of the same degree as $P$. The singularities of this extension are studied.
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| 8. |
- Kiselman, Christer O., 1939-
(author)
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Les mathématiques de Nguyen Thanh Van
- 2011
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In: Annales de la Faculté des Sciences de Toulouse, Mathématiques. - Toulouse : Université Paul Sabatier. - 0240-2963. ; (6) 20:S2, s. 19-32
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Journal article (peer-reviewed)abstract
- Nguyen Thanh Van has done work on analysis in several complex variables, including the theory of holomorphic functions in spaces of infinite dimension. In the article his mathematical work as well as his cooperation with Vietnam is summarized.
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| 9. |
- Samuelsson, Håkan, 1976
(author)
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Integral representation of moderate cohomology
- 2021
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In: Annales de la Faculté des sciences de Toulouse. - : Cellule MathDoc/CEDRAM. - 2258-7519. ; 30, s. 117-137
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Journal article (peer-reviewed)abstract
- We make the classical Dickenstein–Sessa canonical representation in local moderate cohomology explicit by an integral formula. We also provide a similar representation of the higher local moderate cohomology groups.
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| 10. |
- Wulcan, Elizabeth, 1978
(author)
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On a representation of the fundamental class of an ideal due to Lejeune-Jalabert
- 2016
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In: Annales de la Faculté des Sciences de Toulouse. - 2258-7519. ; 25:5, s. 1051-1078
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Journal article (peer-reviewed)abstract
- Lejeune-Jalabert showed that the fundamental class of a Cohen-Macaulay ideal $\a\subset \Ok_0$ admits a representation as a residue, constructed from a free resolution of $\a$, multiplied by a certain differential form coming from the resolution. We give an explicit description of this differential form in the case when the free resolution is the Scarf resolution of a generic monomial ideal. As a consequence we get a new proof and a refinement of Lejeune-Jalabert's result in this case.
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