MYKOLAIV DISTRICT, Ukraine — In their summer campaign to drive Russian troops out of the southern Kherson region, Ukrainian forces have decimated Russian command centers and ammunition depots, cut supply lines with precision strikes on key bridges and terrorized allies officials. of car bombings, shootings and, Ukrainian officials said, at least one poisoning. But out in the sun-scorched fields along the western border of Kherson Oblast, the Ukrainian fighters who will be called upon to deliver the knockout blow in any successful attempt to retake territory remain entrenched in their trenches. Cuts to Russian supply lines have yet to erode Moscow’s forces’ overwhelming advantage in artillery, ammunition and heavy weaponry, making it difficult if not impossible for Ukrainian forces to advance without suffering massive casualties. “We definitely need a counterattack, I honestly believe it will come,” said a 33-year-old lieutenant with the call sign Ada, who commands a trench outpost in the neighboring Mykolaiv region, a few miles from Russian lines in Kherson. But he added: “We need the advantage in numbers, we need the advantage in heavy weapons. Unfortunately, that’s a bit of a problem for us.” Although Ukrainian troops have not advanced in Kherson for weeks, their artillery campaign appears to be paying off, slowing the flow of Russian weapons, equipment and troops into the region, Ukrainian officials say. Using high-precision weapons such as the American-supplied High Mobility Artillery Missile System, or HIMARS, Ukrainian forces pounded the three bridges over the massive Dnipro River that connect thousands of Russians to their supply lines in occupied Ukrainian territory east of the river . The strikes have rendered those bridges “inoperative,” said Natalia Gumeniuk, a spokeswoman for the Ukrainian military’s southern command. Over the weekend, Ukrainian forces launched another strike on the Antonivsky Bridge, the main supply artery to the city of Kherson. “We clearly understand that the occupiers depend on these arteries to continue to bring in supplies and ammunition and military equipment,” Ms Gumenyuk said. The question now is whether this strain on Russia’s supply lines will be enough to cripple the combat capability of Russian troops and perhaps force the Kremlin to order at least part of the force to withdraw from the Kherson and fall back across the river. Several Ukrainian officials in the region said this week that some Russian field commanders had already begun moving their headquarters east of the river, although two senior Ukrainian military officials said there was no evidence of that. At the front, a barrage of Russian strikes inevitably kills a handful of Ada troops each day, the lieutenant said. A near miss from a grad rocket a day earlier had charred the grass around a dugout position, and in a nearby field, the tail section of another rocket could be seen sticking out of the ground. Periodically, a low-decibel thump echoed across the plains. It is the same along the entire 50-mile long front of the Chersona, which cuts roughly from north to south through fertile fields. Ukrainian commanders and military analysts say any forward launch would require far more troops and equipment than Ukraine currently has in the Kherson theater. Refugees from Kherson cut clothes to use as camouflage for Ukrainian troops near Mykolaiv last month. Credit…Daniel Berehulak for The New York Times Russia, meanwhile, has shifted resources from fighting in eastern Donbas to bolster its positions in the south. Major General Dmytro Marchenko, the commander of Ukraine’s forces in the region, recently acknowledged deep frustration with the slow pace of Ukraine’s efforts to retake Kherson, but said he could not give a timetable for the launch of major offensives. “I want to tell the people of Kherson to be a little patient – it won’t be as long as everyone expects,” General Marchenko said in an interview last week with RBK-Ukraine. “We have not forgotten them, no one will abandon our people and we will come to help them, but they must wait a little longer.” If the Ukrainians manage to completely cut the bridges over the Dnipro and keep them cut, the Kremlin will have no choice but to withdraw some forces or force Russian troops to fight with limited supplies and “hope to cope,” said Phillips P. O’Brien. , professor of strategic studies at the University of St. Andrews in Scotland. “If they haven’t built up significant stockpiles on the west bank, you’d think they’d be in big trouble in a few weeks,” he said.