We present the results of the search for spherical volumes containing no galaxies with luminosities brighter than the Magellanic Clouds in the Local Supercluster and its vicinity .
Within a distance of 40 Mpc from us , 89 cosmic voids were discovered with the diameters of 24 to 12 Mpc , containing no galaxies with absolute magnitudes brighter than M _ { K } < -18.4 .
A list of these voids and the sky distribution maps are given .
It was found that 93 % of spherical voids overlap , forming three more extended percolated voids ( hypervoids ) .
The largest of them , HV1 , has 56 initial spherical cells and extends in a horseshoe shape , enveloping the Local Volume and the Virgo cluster .
The Local Void ( Tully , 1988 ) in the Hercules–Aquila region is the closest part of the HV1 .
Another hypervoid , HV2 , contains 22 spherical voids in the Eridanus constellation , and the third compact hypervoid ( HV3 ) comprises 6 spherical cells in the Bootes .
The total volume of these voids incorporates about 30 % of the Local Universe .
Among 2906 dwarf galaxies excluded from the original sample ( n = 10502 ) in the search for spherical volumes , only 68 are located in the voids we have discovered .
They are characterized by late morphological types ( 85 % are Ir , Im , BCD , Sm ) , absolute magnitudes M _ { B } ranging from -13.0 to -16.7 , moderate star formation rates ( \log { SSFR } \sim - 10 \leavevmode \nobreak M _ { \odot } { yr } ^ { -1 } L _ { \odot } ^ { -1 } ) and gas reserves per luminosity unit twice to three times larger than in the other dwarf galaxies located in normal environments .
The dwarf population of the voids shows a certain tendency to sit shallow near the surfaces of cosmic voids . Keywords : cosmology : large-scale structure of Universe .